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How to use it?
Least common denominator:
((y^2-49)/(y^2-14*y+49))^4/((y+7)/(y-7))^4
x*((x-1)^2/x^2)*(2/x-2*(x-1)/x^2)/(x-1)
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sin(2*x)/2)/2-2*cos(x)+x
Factor polynomial:
y^2-x+1
x-x^3+5*x^2/2
x-x^3/3+x^5/5+3*x^4/4
x-x^3/3+x^4/4
Factor squared:
-y^2+y-7
-y^2+y+9
-y^2-y-8
-y^2+y-5
How do you in partial fractions?:
(x^4-x^2)/(x-1)
x^2+1/(x^2)
(m-(14*m-49)/m)/(7/m-1)
e^x/(e^x+2)
Identical expressions
x^cos(one /x)*(cos(one /x)/x+log(x)*sin(one /x)/x^ two)
x to the power of co sinus of e of (1 divide by x) multiply by ( co sinus of e of (1 divide by x) divide by x plus logarithm of (x) multiply by sinus of (1 divide by x) divide by x squared )
x to the power of co sinus of e of (one divide by x) multiply by ( co sinus of e of (one divide by x) divide by x plus logarithm of (x) multiply by sinus of (one divide by x) divide by x to the power of two)
xcos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x2)
xcos1/x*cos1/x/x+logx*sin1/x/x2
x^cos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x²)
x to the power of cos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x to the power of 2)
x^cos(1/x)(cos(1/x)/x+log(x)sin(1/x)/x^2)
xcos(1/x)(cos(1/x)/x+log(x)sin(1/x)/x2)
xcos1/xcos1/x/x+logxsin1/x/x2
x^cos1/xcos1/x/x+logxsin1/x/x^2
x^cos(1 divide by x)*(cos(1 divide by x) divide by x+log(x)*sin(1 divide by x) divide by x^2)
Similar expressions
x^cos(1/x)*(cos(1/x)/x-log(x)*sin(1/x)/x^2)

Expression simplification/ Least common denominator/ x^cos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x^2)

Least common denominator x^cos(1/x)(cos(1/x)/x+log(x)sin(1/x)/x^2)

The solution

You have entered [src]

    /1\ /   /1\             /1\\
 cos|-| |cos|-|   log(x)*sin|-||
    \x/ |   \x/             \x/|
x      *|------ + -------------|
        |  x             2     |
        \               x      /

$$x^{\cos{\left(\frac{1}{x} \right)}} \left(\frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}} + \frac{\cos{\left(\frac{1}{x} \right)}}{x}\right)$$

x^cos(1/x)*(cos(1/x)/x + (log(x)*sin(1/x))/x^2)

General simplification [src]

         /1\                           
 -2 + cos|-|                           
         \x/ /     /1\             /1\\
x           *|x*cos|-| + log(x)*sin|-||
             \     \x/             \x//

$$x^{\cos{\left(\frac{1}{x} \right)} - 2} \left(x \cos{\left(\frac{1}{x} \right)} + \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}\right)$$

x^(-2 + cos(1/x))*(x*cos(1/x) + log(x)*sin(1/x))

Numerical answer [src]

x^cos(1/x)*(cos(1/x)/x + log(x)*sin(1/x)/x^2)

x^cos(1/x)*(cos(1/x)/x + log(x)*sin(1/x)/x^2)

Combining rational expressions [src]

    /1\                           
 cos|-|                           
    \x/ /     /1\             /1\\
x      *|x*cos|-| + log(x)*sin|-||
        \     \x/             \x//
----------------------------------
                 2                
                x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \left(x \cos{\left(\frac{1}{x} \right)} + \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}\right)}{x^{2}}$$

x^cos(1/x)*(x*cos(1/x) + log(x)*sin(1/x))/x^2

Rational denominator [src]

    /1\                              
 cos|-|                              
    \x/ / 2    /1\               /1\\
x      *|x *cos|-| + x*log(x)*sin|-||
        \      \x/               \x//
-------------------------------------
                   3                 
                  x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \left(x^{2} \cos{\left(\frac{1}{x} \right)} + x \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}\right)}{x^{3}}$$

x^cos(1/x)*(x^2*cos(1/x) + x*log(x)*sin(1/x))/x^3

Common denominator [src]

      /1\              /1\              
   cos|-|           cos|-|              
      \x/    /1\       \x/           /1\
x*x      *cos|-| + x      *log(x)*sin|-|
             \x/                     \x/
----------------------------------------
                    2                   
                   x

$$\frac{x x^{\cos{\left(\frac{1}{x} \right)}} \cos{\left(\frac{1}{x} \right)} + x^{\cos{\left(\frac{1}{x} \right)}} \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}$$

(x*x^cos(1/x)*cos(1/x) + x^cos(1/x)*log(x)*sin(1/x))/x^2

Combinatorics [src]

    /1\                           
 cos|-|                           
    \x/ /     /1\             /1\\
x      *|x*cos|-| + log(x)*sin|-||
        \     \x/             \x//
----------------------------------
                 2                
                x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \left(x \cos{\left(\frac{1}{x} \right)} + \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}\right)}{x^{2}}$$

x^cos(1/x)*(x*cos(1/x) + log(x)*sin(1/x))/x^2

Powers [src]

  I    -I  / I    -I                          \
  -    --- | -    ---                         |
  x     x  | x     x      /   -I     I\       |
 e    e    |e    e        |   ---    -|       |
 -- + ---- |-- + ----     |    x     x|       |
 2     2   |2     2     I*\- e    + e /*log(x)|
x         *|--------- - ----------------------|
           |    x                   2         |
           \                     2*x          /

$$x^{\frac{e^{\frac{i}{x}}}{2} + \frac{e^{- \frac{i}{x}}}{2}} \left(\frac{\frac{e^{\frac{i}{x}}}{2} + \frac{e^{- \frac{i}{x}}}{2}}{x} - \frac{i \left(e^{\frac{i}{x}} - e^{- \frac{i}{x}}\right) \log{\left(x \right)}}{2 x^{2}}\right)$$

    /1\ /   /1\             /1\\
 cos|-| |cos|-|   log(x)*sin|-||
    \x/ |   \x/             \x/|
x      *|------ + -------------|
        |  x             2     |
        \               x      /

$$x^{\cos{\left(\frac{1}{x} \right)}} \left(\frac{\cos{\left(\frac{1}{x} \right)}}{x} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}\right)$$

x^cos(1/x)*(cos(1/x)/x + log(x)*sin(1/x)/x^2)

Assemble expression [src]

    /1\ /   /1\             /1\\
 cos|-| |cos|-|   log(x)*sin|-||
    \x/ |   \x/             \x/|
x      *|------ + -------------|
        |  x             2     |
        \               x      /

$$x^{\cos{\left(\frac{1}{x} \right)}} \left(\frac{\cos{\left(\frac{1}{x} \right)}}{x} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}\right)$$

x^cos(1/x)*(cos(1/x)/x + log(x)*sin(1/x)/x^2)

Expand expression [src]

    /1\              /1\              
 cos|-|           cos|-|              
    \x/    /1\       \x/           /1\
x      *cos|-|   x      *log(x)*sin|-|
           \x/                     \x/
-------------- + ---------------------
      x                     2         
                           x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \cos{\left(\frac{1}{x} \right)}}{x} + \frac{x^{\cos{\left(\frac{1}{x} \right)}} \log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}$$

x^cos(1/x)*cos(1/x)/x + x^cos(1/x)*log(x)*sin(1/x)/x^2

Trigonometric part [src]

   1                          
 ------                       
    /1\                       
 sec|-|                       
    \x/ /   1         log(x) \
x      *|-------- + ---------|
        |     /1\    2    /1\|
        |x*sec|-|   x *csc|-||
        \     \x/         \x//

$$x^{\frac{1}{\sec{\left(\frac{1}{x} \right)}}} \left(\frac{1}{x \sec{\left(\frac{1}{x} \right)}} + \frac{\log{\left(x \right)}}{x^{2} \csc{\left(\frac{1}{x} \right)}}\right)$$

    /1   pi\ /   /1   pi\             /1\\
 sin|- + --| |sin|- + --|   log(x)*sin|-||
    \x   2 / |   \x   2 /             \x/|
x           *|----------- + -------------|
             |     x               2     |
             \                    x      /

$$x^{\sin{\left(\frac{\pi}{2} + \frac{1}{x} \right)}} \left(\frac{\sin{\left(\frac{\pi}{2} + \frac{1}{x} \right)}}{x} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}\right)$$

    /1   pi\ /          /1\              \
 sin|- + --| |log(x)*sin|-|              |
    \x   2 / |          \x/      /1   pi\|
x           *|------------- + sin|- + --||
             \      x            \x   2 //
------------------------------------------
                    x

$$\frac{x^{\sin{\left(\frac{\pi}{2} + \frac{1}{x} \right)}} \left(\sin{\left(\frac{\pi}{2} + \frac{1}{x} \right)} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x}\right)}{x}$$

        2/ 1 \                                         
 1 - tan |---|                                         
         \2*x/                                         
 -------------                                         
        2/ 1 \ /         2/ 1 \                 / 1 \ \
 1 + tan |---| |  1 - tan |---|     2*log(x)*tan|---| |
         \2*x/ |          \2*x/                 \2*x/ |
x             *|----------------- + ------------------|
               |  /       2/ 1 \\    2 /       2/ 1 \\|
               |x*|1 + tan |---||   x *|1 + tan |---|||
               \  \        \2*x//      \        \2*x///

$$x^{\frac{1 - \tan^{2}{\left(\frac{1}{2 x} \right)}}{\tan^{2}{\left(\frac{1}{2 x} \right)} + 1}} \left(\frac{1 - \tan^{2}{\left(\frac{1}{2 x} \right)}}{x \left(\tan^{2}{\left(\frac{1}{2 x} \right)} + 1\right)} + \frac{2 \log{\left(x \right)} \tan{\left(\frac{1}{2 x} \right)}}{x^{2} \left(\tan^{2}{\left(\frac{1}{2 x} \right)} + 1\right)}\right)$$

         2/ 1 \                                         
 -1 + cot |---|                                         
          \2*x/                                         
 --------------                                         
        2/ 1 \  /          2/ 1 \         / 1 \        \
 1 + cot |---|  |  -1 + cot |---|    2*cot|---|*log(x) |
         \2*x/  |           \2*x/         \2*x/        |
x              *|----------------- + ------------------|
                |  /       2/ 1 \\    2 /       2/ 1 \\|
                |x*|1 + cot |---||   x *|1 + cot |---|||
                \  \        \2*x//      \        \2*x///

$$x^{\frac{\cot^{2}{\left(\frac{1}{2 x} \right)} - 1}{\cot^{2}{\left(\frac{1}{2 x} \right)} + 1}} \left(\frac{\cot^{2}{\left(\frac{1}{2 x} \right)} - 1}{x \left(\cot^{2}{\left(\frac{1}{2 x} \right)} + 1\right)} + \frac{2 \log{\left(x \right)} \cot{\left(\frac{1}{2 x} \right)}}{x^{2} \left(\cot^{2}{\left(\frac{1}{2 x} \right)} + 1\right)}\right)$$

    /1\ /   /1   pi\                \
 cos|-| |cos|- - --|*log(x)         |
    \x/ |   \x   2 /             /1\|
x      *|------------------ + cos|-||
        \        x               \x//
-------------------------------------
                  x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \left(\cos{\left(\frac{1}{x} \right)} + \frac{\log{\left(x \right)} \cos{\left(- \frac{\pi}{2} + \frac{1}{x} \right)}}{x}\right)}{x}$$

         2/ 1 \                                     
 -1 + cot |---|                                     
          \2*x/                                     
 --------------                                     
        2/ 1 \  /        2/ 1 \        / 1 \       \
 1 + cot |---|  |-1 + cot |---|   2*cot|---|*log(x)|
         \2*x/  |         \2*x/        \2*x/       |
x              *|-------------- + -----------------|
                |       2/ 1 \      /       2/ 1 \\|
                |1 + cot |---|    x*|1 + cot |---|||
                \        \2*x/      \        \2*x///
----------------------------------------------------
                         x

$$\frac{x^{\frac{\cot^{2}{\left(\frac{1}{2 x} \right)} - 1}{\cot^{2}{\left(\frac{1}{2 x} \right)} + 1}} \left(\frac{\cot^{2}{\left(\frac{1}{2 x} \right)} - 1}{\cot^{2}{\left(\frac{1}{2 x} \right)} + 1} + \frac{2 \log{\left(x \right)} \cot{\left(\frac{1}{2 x} \right)}}{x \left(\cot^{2}{\left(\frac{1}{2 x} \right)} + 1\right)}\right)}{x}$$

      1                                 
 -----------                            
    /pi   1\                            
 csc|-- - -|                            
    \2    x/ /      1           log(x) \
x           *|------------- + ---------|
             |     /pi   1\    2    /1\|
             |x*csc|-- - -|   x *csc|-||
             \     \2    x/         \x//

$$x^{\frac{1}{\csc{\left(\frac{\pi}{2} - \frac{1}{x} \right)}}} \left(\frac{1}{x \csc{\left(\frac{\pi}{2} - \frac{1}{x} \right)}} + \frac{\log{\left(x \right)}}{x^{2} \csc{\left(\frac{1}{x} \right)}}\right)$$

    /1\ /          /1\         \
 cos|-| |log(x)*sin|-|         |
    \x/ |          \x/      /1\|
x      *|------------- + cos|-||
        \      x            \x//
--------------------------------
               x

$$\frac{x^{\cos{\left(\frac{1}{x} \right)}} \left(\cos{\left(\frac{1}{x} \right)} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x}\right)}{x}$$

   1                               
 ------                            
    /1\                            
 sec|-|                            
    \x/ /   1           log(x)    \
x      *|-------- + --------------|
        |     /1\    2    /1   pi\|
        |x*sec|-|   x *sec|- - --||
        \     \x/         \x   2 //

$$x^{\frac{1}{\sec{\left(\frac{1}{x} \right)}}} \left(\frac{1}{x \sec{\left(\frac{1}{x} \right)}} + \frac{\log{\left(x \right)}}{x^{2} \sec{\left(- \frac{\pi}{2} + \frac{1}{x} \right)}}\right)$$

      1                              
 -----------                         
    /pi   1\                         
 csc|-- - -|                         
    \2    x/ /     1         log(x) \
x           *|----------- + --------|
             |   /pi   1\        /1\|
             |csc|-- - -|   x*csc|-||
             \   \2    x/        \x//
-------------------------------------
                  x

$$\frac{x^{\frac{1}{\csc{\left(\frac{\pi}{2} - \frac{1}{x} \right)}}} \left(\frac{1}{\csc{\left(\frac{\pi}{2} - \frac{1}{x} \right)}} + \frac{\log{\left(x \right)}}{x \csc{\left(\frac{1}{x} \right)}}\right)}{x}$$

    /1\ /   /1\             /1\\
 cos|-| |cos|-|   log(x)*sin|-||
    \x/ |   \x/             \x/|
x      *|------ + -------------|
        |  x             2     |
        \               x      /

$$x^{\cos{\left(\frac{1}{x} \right)}} \left(\frac{\cos{\left(\frac{1}{x} \right)}}{x} + \frac{\log{\left(x \right)} \sin{\left(\frac{1}{x} \right)}}{x^{2}}\right)$$

   1                            
 ------                         
    /1\                         
 sec|-|                         
    \x/ /  1          log(x)   \
x      *|------ + -------------|
        |   /1\        /1   pi\|
        |sec|-|   x*sec|- - --||
        \   \x/        \x   2 //
--------------------------------
               x

$$\frac{x^{\frac{1}{\sec{\left(\frac{1}{x} \right)}}} \left(\frac{1}{\sec{\left(\frac{1}{x} \right)}} + \frac{\log{\left(x \right)}}{x \sec{\left(- \frac{\pi}{2} + \frac{1}{x} \right)}}\right)}{x}$$

    /1\ /   /1\      /1   pi\       \
 cos|-| |cos|-|   cos|- - --|*log(x)|
    \x/ |   \x/      \x   2 /       |
x      *|------ + ------------------|
        |  x               2        |
        \                 x         /

$$x^{\cos{\left(\frac{1}{x} \right)}} \left(\frac{\cos{\left(\frac{1}{x} \right)}}{x} + \frac{\log{\left(x \right)} \cos{\left(- \frac{\pi}{2} + \frac{1}{x} \right)}}{x^{2}}\right)$$

        2/ 1 \                                    
 1 - tan |---|                                    
         \2*x/                                    
 -------------                                    
        2/ 1 \ /       2/ 1 \               / 1 \\
 1 + tan |---| |1 - tan |---|   2*log(x)*tan|---||
         \2*x/ |        \2*x/               \2*x/|
x             *|------------- + -----------------|
               |       2/ 1 \     /       2/ 1 \\|
               |1 + tan |---|   x*|1 + tan |---|||
               \        \2*x/     \        \2*x///
--------------------------------------------------
                        x

$$\frac{x^{\frac{1 - \tan^{2}{\left(\frac{1}{2 x} \right)}}{\tan^{2}{\left(\frac{1}{2 x} \right)} + 1}} \left(\frac{1 - \tan^{2}{\left(\frac{1}{2 x} \right)}}{\tan^{2}{\left(\frac{1}{2 x} \right)} + 1} + \frac{2 \log{\left(x \right)} \tan{\left(\frac{1}{2 x} \right)}}{x \left(\tan^{2}{\left(\frac{1}{2 x} \right)} + 1\right)}\right)}{x}$$

x^((1 - tan(1/(2*x))^2)/(1 + tan(1/(2*x))^2))*((1 - tan(1/(2*x))^2)/(1 + tan(1/(2*x))^2) + 2*log(x)*tan(1/(2*x))/(x*(1 + tan(1/(2*x))^2)))/x

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator x^cos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x^2)

The solution

Least common denominator x^cos(1/x)(cos(1/x)/x+log(x)sin(1/x)/x^2)