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Least common denominator:
(a+1/a+2)/a+1
1/(1+x^2/3)
(z/x-z+x+z/z)/x/x^2-z^2
(z/x-z+x+z/z)/x/x^2-x*z^2
Factor polynomial:
x^4+1
x^3-1^3+3^3-x^3
y^2/2+y^23/23
-x^7+x^6/4+9*x*5/8-9*x^4/32-x^3/8+x^2/32
Factor squared:
y^4-y^2-3
x^2+x-2
y^2-4*y+3
x^2+x-3
How do you in partial fractions?:
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
3/(x^3+5)-9*x^3/(x^3+5)^2
Identical expressions
(sin(four *x)/((two + two *x)* eight)-sin(two *x)/ two +x/ two)/ two
( sinus of (4 multiply by x) divide by ((2 plus 2 multiply by x) multiply by 8) minus sinus of (2 multiply by x) divide by 2 plus x divide by 2) divide by 2
( sinus of (four multiply by x) divide by ((two plus two multiply by x) multiply by eight) minus sinus of (two multiply by x) divide by two plus x divide by two) divide by two
(sin(4x)/((2+2x)8)-sin(2x)/2+x/2)/2
sin4x/2+2x8-sin2x/2+x/2/2
(sin(4*x) divide by ((2+2*x)*8)-sin(2*x) divide by 2+x divide by 2) divide by 2
Similar expressions
(sin(4*x)/((2+2*x)*8)-sin(2*x)/2-x/2)/2
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2
(sin(4*x)/((2-2*x)*8)-sin(2*x)/2+x/2)/2

Expression simplification/ Least common denominator/ (sin(4*x)/((2+2*x)*8)-sin(2*x)/2+x/2)/2

Least common denominator (sin(4x)/((2+2x)8)-sin(2x)/2+x/2)/2

The solution

You have entered [src]

  sin(4*x)    sin(2*x)   x
----------- - -------- + -
(2 + 2*x)*8      2       2
--------------------------
            2

$$\frac{\frac{x}{2} + \left(- \frac{\sin{\left(2 x \right)}}{2} + \frac{\sin{\left(4 x \right)}}{8 \left(2 x + 2\right)}\right)}{2}$$

(sin(4*x)/(((2 + 2*x)*8)) - sin(2*x)/2 + x/2)/2

General simplification [src]

(8 + 8*x)*(x - sin(2*x)) + sin(4*x)
-----------------------------------
             32*(1 + x)

$$\frac{\left(x - \sin{\left(2 x \right)}\right) \left(8 x + 8\right) + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$

((8 + 8*x)*(x - sin(2*x)) + sin(4*x))/(32*(1 + x))

Combinatorics [src]

                       2                          
-8*sin(2*x) + 8*x + 8*x  - 8*x*sin(2*x) + sin(4*x)
--------------------------------------------------
                    32*(1 + x)

$$\frac{8 x^{2} - 8 x \sin{\left(2 x \right)} + 8 x - 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$

(-8*sin(2*x) + 8*x + 8*x^2 - 8*x*sin(2*x) + sin(4*x))/(32*(1 + x))

Powers [src]

  sin(2*x)   x      sin(4*x)  
- -------- + - + -------------
     4       4   2*(16 + 16*x)

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

      /   -2*I*x    2*I*x\     /   -4*I*x    4*I*x\
x   I*\- e       + e     /   I*\- e       + e     /
- + ---------------------- - ----------------------
4             8                  4*(16 + 16*x)

$$\frac{x}{4} + \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{8} - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{4 \left(16 x + 16\right)}$$

x/4 + i*(-exp(-2*i*x) + exp(2*i*x))/8 - i*(-exp(-4*i*x) + exp(4*i*x))/(4*(16 + 16*x))

Common denominator [src]

  sin(2*x)   x    sin(4*x)
- -------- + - + ---------
     4       4   32 + 32*x

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32 x + 32}$$

-sin(2*x)/4 + x/4 + sin(4*x)/(32 + 32*x)

Rational denominator [src]

4*sin(4*x) + x*(32 + 32*x) - 2*(16 + 16*x)*sin(2*x)
---------------------------------------------------
                    128 + 128*x

$$\frac{x \left(32 x + 32\right) - 2 \left(16 x + 16\right) \sin{\left(2 x \right)} + 4 \sin{\left(4 x \right)}}{128 x + 128}$$

(4*sin(4*x) + x*(32 + 32*x) - 2*(16 + 16*x)*sin(2*x))/(128 + 128*x)

Combining rational expressions [src]

-8*(1 + x)*sin(2*x) + 8*x*(1 + x) + sin(4*x)
--------------------------------------------
                 32*(1 + x)

$$\frac{8 x \left(x + 1\right) - 8 \left(x + 1\right) \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$

(-8*(1 + x)*sin(2*x) + 8*x*(1 + x) + sin(4*x))/(32*(1 + x))

Numerical answer [src]

0.25*x - 0.25*sin(2*x) + 0.5*sin(4*x)/(16.0 + 16.0*x)

0.25*x - 0.25*sin(2*x) + 0.5*sin(4*x)/(16.0 + 16.0*x)

Assemble expression [src]

  sin(2*x)   x      sin(4*x)  
- -------- + - + -------------
     4       4   2*(16 + 16*x)

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

-sin(2*x)/4 + x/4 + sin(4*x)/(2*(16 + 16*x))

Trigonometric part [src]

  sin(2*x)   x     sin(4*x)  
- -------- + - + ------------
     4       4   16*(2 + 2*x)

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{16 \left(2 x + 2\right)}$$

      1        x             1           
- ---------- + - + ----------------------
  4*csc(2*x)   4   2*(16 + 16*x)*csc(4*x)

$$\frac{x}{4} - \frac{1}{4 \csc{\left(2 x \right)}} + \frac{1}{2 \left(16 x + 16\right) \csc{\left(4 x \right)}}$$

x        cot(x)                 cot(2*x)         
- - --------------- + ---------------------------
4     /       2   \   /       2     \            
    2*\1 + cot (x)/   \1 + cot (2*x)/*(16 + 16*x)

$$\frac{x}{4} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} + \frac{\cot{\left(2 x \right)}}{\left(16 x + 16\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$

         1          x                1             
- --------------- + - + ---------------------------
       /      pi\   4                    /      pi\
  4*sec|2*x - --|       2*(16 + 16*x)*sec|4*x - --|
       \      2 /                        \      2 /

$$\frac{x}{4} - \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \left(16 x + 16\right) \sec{\left(4 x - \frac{\pi}{2} \right)}}$$

  sin(2*x)   x      sin(4*x)  
- -------- + - + -------------
     4       4   2*(16 + 16*x)

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

     /      pi\          /      pi\
  cos|2*x - --|       cos|4*x - --|
     \      2 /   x      \      2 /
- ------------- + - + -------------
        4         4   2*(16 + 16*x)

$$\frac{x}{4} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} + \frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{2 \left(16 x + 16\right)}$$

x        tan(x)                 tan(2*x)         
- - --------------- + ---------------------------
4     /       2   \   /       2     \            
    2*\1 + tan (x)/   \1 + tan (2*x)/*(16 + 16*x)

$$\frac{x}{4} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{\tan{\left(2 x \right)}}{\left(16 x + 16\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$

x/4 - tan(x)/(2*(1 + tan(x)^2)) + tan(2*x)/((1 + tan(2*x)^2)*(16 + 16*x))

Expand expression [src]

                         3                            
x   cos(x)*sin(x)   4*sin (x)*cos(x)   2*cos(x)*sin(x)
- - ------------- - ---------------- + ---------------
4         2            16 + 16*x          16 + 16*x

$$\frac{x}{4} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{16 x + 16} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{16 x + 16}$$

  sin(2*x)   x     sin(4*x)  
- -------- + - + ------------
     4       4   16*(2 + 2*x)

$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{16 \left(2 x + 2\right)}$$

-sin(2*x)/4 + x/4 + sin(4*x)/(16*(2 + 2*x))

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How to use it?

Identical expressions

Similar expressions

Least common denominator (sin(4*x)/((2+2*x)*8)-sin(2*x)/2+x/2)/2

The solution

Least common denominator (sin(4x)/((2+2x)8)-sin(2x)/2+x/2)/2