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Least common denominator:
x^2*log(x)/2-x^2/4
sqrt(4/x+1)*x+2*log(sqrt(4/x+1)+1)-2*log(sqrt(4/x+1)-1)
atan(tan(f)*sqrt(a^2-1)/a)/sqrt(a^2-1)
(a/5+a/2)*a^2/6
Factor polynomial:
x^6-y^6
x^3+x-2
x^4+x^2+1
x^3+x^2+x+1
Factor squared:
-y^4+y^2-4
x^2+3*y*x+2*y^2
y^4-y^2-2
-y^4+y^2-3
How do you in partial fractions?:
((3*c+1)/(c-1)+c)/(c+1)
z/(z+9)^2-z/(z^2-81)
((z^2-z)/(z^2-9))^-1/(z^2-3*z)/(z-1)
((z)-((7*z)/(z+3)))*((z+3)/(z-4))
Identical expressions
five *(two - two /x^ two)*cos(two *x+ two /x)
5 multiply by (2 minus 2 divide by x squared ) multiply by co sinus of e of (2 multiply by x plus 2 divide by x)
five multiply by (two minus two divide by x to the power of two) multiply by co sinus of e of (two multiply by x plus two divide by x)
5*(2-2/x2)*cos(2*x+2/x)
5*2-2/x2*cos2*x+2/x
5*(2-2/x²)*cos(2*x+2/x)
5*(2-2/x to the power of 2)*cos(2*x+2/x)
5(2-2/x^2)cos(2x+2/x)
5(2-2/x2)cos(2x+2/x)
52-2/x2cos2x+2/x
52-2/x^2cos2x+2/x
5*(2-2 divide by x^2)*cos(2*x+2 divide by x)
Similar expressions
5*(2-2/x^2)*cos(2*x-2/x)
5*(2+2/x^2)*cos(2*x+2/x)

Expression simplification/ Least common denominator/ 5*(2-2/x^2)*cos(2*x+2/x)

Least common denominator 5(2-2/x^2)cos(2*x+2/x)

The solution

You have entered [src]

  /    2 \    /      2\
5*|2 - --|*cos|2*x + -|
  |     2|    \      x/
  \    x /

$$5 \left(2 - \frac{2}{x^{2}}\right) \cos{\left(2 x + \frac{2}{x} \right)}$$

(5*(2 - 2/x^2))*cos(2*x + 2/x)

General simplification [src]

   /      2\    /      2\
10*\-1 + x /*cos|2*x + -|
                \      x/
-------------------------
             2           
            x

$$\frac{10 \left(x^{2} - 1\right) \cos{\left(2 x + \frac{2}{x} \right)}}{x^{2}}$$

10*(-1 + x^2)*cos(2*x + 2/x)/x^2

Powers [src]

          /   /       2\      /      2\\
          | I*|-2*x - -|    I*|2*x + -||
          |   \       x/      \      x/|
/     10\ |e               e           |
|10 - --|*|------------- + ------------|
|      2| \      2              2      /
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \left(\frac{e^{i \left(- 2 x - \frac{2}{x}\right)}}{2} + \frac{e^{i \left(2 x + \frac{2}{x}\right)}}{2}\right)$$

/     10\    /      2\
|10 - --|*cos|2*x + -|
|      2|    \      x/
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \cos{\left(2 x + \frac{2}{x} \right)}$$

(10 - 10/x^2)*cos(2*x + 2/x)

Numerical answer [src]

(10.0 - 10.0/x^2)*cos(2*x + 2/x)

(10.0 - 10.0/x^2)*cos(2*x + 2/x)

Assemble expression [src]

/     10\    /      2\
|10 - --|*cos|2*x + -|
|      2|    \      x/
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \cos{\left(2 x + \frac{2}{x} \right)}$$

(10 - 10/x^2)*cos(2*x + 2/x)

Rational denominator [src]

   /      2\    /      2\
10*\-1 + x /*cos|2*x + -|
                \      x/
-------------------------
             2           
            x

$$\frac{10 \left(x^{2} - 1\right) \cos{\left(2 x + \frac{2}{x} \right)}}{x^{2}}$$

10*(-1 + x^2)*cos(2*x + 2/x)/x^2

Common denominator [src]

                        /      2\
                  10*cos|2*x + -|
      /      2\         \      x/
10*cos|2*x + -| - ---------------
      \      x/           2      
                         x

$$10 \cos{\left(2 x + \frac{2}{x} \right)} - \frac{10 \cos{\left(2 x + \frac{2}{x} \right)}}{x^{2}}$$

10*cos(2*x + 2/x) - 10*cos(2*x + 2/x)/x^2

Combinatorics [src]

                       /      2\
10*(1 + x)*(-1 + x)*cos|2*x + -|
                       \      x/
--------------------------------
                2               
               x

$$\frac{10 \left(x - 1\right) \left(x + 1\right) \cos{\left(2 x + \frac{2}{x} \right)}}{x^{2}}$$

10*(1 + x)*(-1 + x)*cos(2*x + 2/x)/x^2

Trigonometric part [src]

/     10\    /  /    1\\
|10 - --|*cos|2*|x + -||
|      2|    \  \    x//
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \cos{\left(2 \left(x + \frac{1}{x}\right) \right)}$$

/         4/    1\\          
|    4*sin |x + -||          
|          \    x/| /     10\
|1 - -------------|*|10 - --|
|       2/      2\| |      2|
|    sin |2*x + -|| \     x /
\        \      x//          
-----------------------------
               4/    1\      
          4*sin |x + -|      
                \    x/      
      1 + -------------      
             2/      2\      
          sin |2*x + -|      
              \      x/

$$\frac{\left(10 - \frac{10}{x^{2}}\right) \left(- \frac{4 \sin^{4}{\left(x + \frac{1}{x} \right)}}{\sin^{2}{\left(2 x + \frac{2}{x} \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(x + \frac{1}{x} \right)}}{\sin^{2}{\left(2 x + \frac{2}{x} \right)}} + 1}$$

/          4/    1\ \          
|     4*sin |x + -| |          
|           \    x/ | /     10\
|1 - ---------------|*|10 - --|
|       2/  /    1\\| |      2|
|    sin |2*|x + -||| \     x /
\        \  \    x///          
-------------------------------
                4/    1\       
           4*sin |x + -|       
                 \    x/       
      1 + ---------------      
             2/  /    1\\      
          sin |2*|x + -||      
              \  \    x//

$$\frac{\left(10 - \frac{10}{x^{2}}\right) \left(- \frac{4 \sin^{4}{\left(x + \frac{1}{x} \right)}}{\sin^{2}{\left(2 \left(x + \frac{1}{x}\right) \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(x + \frac{1}{x} \right)}}{\sin^{2}{\left(2 \left(x + \frac{1}{x}\right) \right)}} + 1}$$

/       2/    1\\ /     10\
|1 - tan |x + -||*|10 - --|
\        \    x// |      2|
                  \     x /
---------------------------
             2/    1\      
      1 + tan |x + -|      
              \    x/

$$\frac{\left(1 - \tan^{2}{\left(x + \frac{1}{x} \right)}\right) \left(10 - \frac{10}{x^{2}}\right)}{\tan^{2}{\left(x + \frac{1}{x} \right)} + 1}$$

/         2/    1\   \          
|      sec |x + -|   |          
|          \    x/   | /     10\
|1 - ----------------|*|10 - --|
|       2/    1   pi\| |      2|
|    sec |x + - - --|| \     x /
\        \    x   2 //          
--------------------------------
               2/    1\         
            sec |x + -|         
                \    x/         
      1 + ----------------      
             2/    1   pi\      
          sec |x + - - --|      
              \    x   2 /

$$\frac{\left(10 - \frac{10}{x^{2}}\right) \left(- \frac{\sec^{2}{\left(x + \frac{1}{x} \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} + \frac{1}{x} \right)}} + 1\right)}{\frac{\sec^{2}{\left(x + \frac{1}{x} \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} + \frac{1}{x} \right)}} + 1}$$

/       2/pi       1\\          
|    csc |-- - x - -||          
|        \2        x/| /     10\
|1 - ----------------|*|10 - --|
|         2/    1\   | |      2|
|      csc |x + -|   | \     x /
\          \    x/   /          
--------------------------------
             2/pi       1\      
          csc |-- - x - -|      
              \2        x/      
      1 + ----------------      
               2/    1\         
            csc |x + -|         
                \    x/

$$\frac{\left(1 - \frac{\csc^{2}{\left(- x + \frac{\pi}{2} - \frac{1}{x} \right)}}{\csc^{2}{\left(x + \frac{1}{x} \right)}}\right) \left(10 - \frac{10}{x^{2}}\right)}{1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} - \frac{1}{x} \right)}}{\csc^{2}{\left(x + \frac{1}{x} \right)}}}$$

/     10\    /pi         2\
|10 - --|*sin|-- + 2*x + -|
|      2|    \2          x/
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \sin{\left(2 x + \frac{\pi}{2} + \frac{2}{x} \right)}$$

       10   
  10 - --   
        2   
       x    
------------
   /      2\
sec|2*x + -|
   \      x/

$$\frac{10 - \frac{10}{x^{2}}}{\sec{\left(2 x + \frac{2}{x} \right)}}$$

/     10\    /      2\
|10 - --|*cos|2*x + -|
|      2|    \      x/
\     x /

$$\left(10 - \frac{10}{x^{2}}\right) \cos{\left(2 x + \frac{2}{x} \right)}$$

/        2/    1\\ /     10\
|-1 + cot |x + -||*|10 - --|
\         \    x// |      2|
                   \     x /
----------------------------
             2/    1\       
      1 + cot |x + -|       
              \    x/

$$\frac{\left(10 - \frac{10}{x^{2}}\right) \left(\cot^{2}{\left(x + \frac{1}{x} \right)} - 1\right)}{\cot^{2}{\left(x + \frac{1}{x} \right)} + 1}$$

/       2/    1   pi\\          
|    cos |x + - - --||          
|        \    x   2 /| /     10\
|1 - ----------------|*|10 - --|
|         2/    1\   | |      2|
|      cos |x + -|   | \     x /
\          \    x/   /          
--------------------------------
             2/    1   pi\      
          cos |x + - - --|      
              \    x   2 /      
      1 + ----------------      
               2/    1\         
            cos |x + -|         
                \    x/

$$\frac{\left(1 - \frac{\cos^{2}{\left(x - \frac{\pi}{2} + \frac{1}{x} \right)}}{\cos^{2}{\left(x + \frac{1}{x} \right)}}\right) \left(10 - \frac{10}{x^{2}}\right)}{1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} + \frac{1}{x} \right)}}{\cos^{2}{\left(x + \frac{1}{x} \right)}}}$$

          10     
     10 - --     
           2     
          x      
-----------------
   /pi         2\
csc|-- - 2*x - -|
   \2          x/

$$\frac{10 - \frac{10}{x^{2}}}{\csc{\left(- 2 x + \frac{\pi}{2} - \frac{2}{x} \right)}}$$

/         1     \ /     10\
|1 - -----------|*|10 - --|
|       2/    1\| |      2|
|    cot |x + -|| \     x /
\        \    x//          
---------------------------
               1           
      1 + -----------      
             2/    1\      
          cot |x + -|      
              \    x/

$$\frac{\left(1 - \frac{1}{\cot^{2}{\left(x + \frac{1}{x} \right)}}\right) \left(10 - \frac{10}{x^{2}}\right)}{1 + \frac{1}{\cot^{2}{\left(x + \frac{1}{x} \right)}}}$$

(1 - 1/cot(x + 1/x)^2)*(10 - 10/x^2)/(1 + cot(x + 1/x)^(-2))

Expand expression [src]

                                                       2/1\                              2       2/1\                                                 /1\           /1\
                                          2      20*cos |-|                        40*cos (x)*cos |-|                                    40*cos(x)*cos|-|*sin(x)*sin|-|
           2            2/1\   10   20*cos (x)          \x/         2       2/1\                  \x/                /1\           /1\                \x/           \x/
10 - 20*cos (x) - 20*cos |-| - -- + ---------- + ---------- + 40*cos (x)*cos |-| - ------------------ - 40*cos(x)*cos|-|*sin(x)*sin|-| + ------------------------------
                         \x/    2        2            2                      \x/            2                        \x/           \x/                  2              
                               x        x            x                                     x                                                           x

$$- 40 \sin{\left(\frac{1}{x} \right)} \sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)} \cos{\left(x \right)} + 40 \cos^{2}{\left(\frac{1}{x} \right)} \cos^{2}{\left(x \right)} - 20 \cos^{2}{\left(\frac{1}{x} \right)} - 20 \cos^{2}{\left(x \right)} + 10 + \frac{40 \sin{\left(\frac{1}{x} \right)} \sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)} \cos{\left(x \right)}}{x^{2}} - \frac{40 \cos^{2}{\left(\frac{1}{x} \right)} \cos^{2}{\left(x \right)}}{x^{2}} + \frac{20 \cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}} + \frac{20 \cos^{2}{\left(x \right)}}{x^{2}} - \frac{10}{x^{2}}$$

10 - 20*cos(x)^2 - 20*cos(1/x)^2 - 10/x^2 + 20*cos(x)^2/x^2 + 20*cos(1/x)^2/x^2 + 40*cos(x)^2*cos(1/x)^2 - 40*cos(x)^2*cos(1/x)^2/x^2 - 40*cos(x)*cos(1/x)*sin(x)*sin(1/x) + 40*cos(x)*cos(1/x)*sin(x)*sin(1/x)/x^2

Combining rational expressions [src]

                /  /     2\\
   /      2\    |2*\1 + x /|
10*\-1 + x /*cos|----------|
                \    x     /
----------------------------
              2             
             x

$$\frac{10 \left(x^{2} - 1\right) \cos{\left(\frac{2 \left(x^{2} + 1\right)}{x} \right)}}{x^{2}}$$

10*(-1 + x^2)*cos(2*(1 + x^2)/x)/x^2

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator 5*(2-2/x^2)*cos(2*x+2/x)

The solution

Least common denominator 5(2-2/x^2)cos(2*x+2/x)