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Least common denominator:
4*((sin(8*x)/2+4*x)/8-sin(4*x)/2+x)
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
2/(a+2)+(a-2)/(a^2+4*a+4)/(a/(2*a-4)+(a^2+4)/(8-2*a)-2/(2*a+a^2))
(z+z/q)*(z-z/q)
Factor polynomial:
x^3-8
x^2+x-6
x^2+4
x^3+1
Factor squared:
y^4+y^2+3
-y^4+y^2+14
y^4-y^2+15
y^4-y^2+3
How do you in partial fractions?:
(z/c+c/z)/((z^2+c^2)/(5*z^9*c))
(x^2-9)/(x+3)
(x+5)/(x^2+22*x+85)
(x^2-x-12)/(x+3)
Identical expressions
(sin(four *x)/((two + two *x)* eight)+sin(two *x)/ two +x/ two)/ two -x/ sixteen +sin(four *x)/ thirty-two
( sinus of (4 multiply by x) divide by ((2 plus 2 multiply by x) multiply by 8) plus sinus of (2 multiply by x) divide by 2 plus x divide by 2) divide by 2 minus x divide by 16 plus sinus of (4 multiply by x) divide by 32
( sinus of (four multiply by x) divide by ((two plus two multiply by x) multiply by eight) plus sinus of (two multiply by x) divide by two plus x divide by two) divide by two minus x divide by sixteen plus sinus of (four multiply by x) divide by thirty minus two
(sin(4x)/((2+2x)8)+sin(2x)/2+x/2)/2-x/16+sin(4x)/32
sin4x/2+2x8+sin2x/2+x/2/2-x/16+sin4x/32
(sin(4*x) divide by ((2+2*x)*8)+sin(2*x) divide by 2+x divide by 2) divide by 2-x divide by 16+sin(4*x) divide by 32
Similar expressions
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2-x/2)/2-x/16+sin(4*x)/32
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2+x/16+sin(4*x)/32
(sin(4*x)/((2-2*x)*8)+sin(2*x)/2+x/2)/2-x/16+sin(4*x)/32
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2-x/16-sin(4*x)/32
(sin(4*x)/((2+2*x)*8)-sin(2*x)/2+x/2)/2-x/16+sin(4*x)/32

Expression simplification/ Least common denominator/ (sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2-x/16+sin(4*x)/32

Least common denominator (sin(4x)/((2+2x)8)+sin(2x)/2+x/2)/2-x/16+sin(4*x)/32

The solution

You have entered [src]

  sin(4*x)    sin(2*x)   x                
----------- + -------- + -                
(2 + 2*x)*8      2       2   x    sin(4*x)
-------------------------- - -- + --------
            2                16      32

$$\left(- \frac{x}{16} + \frac{\frac{x}{2} + \left(\frac{\sin{\left(2 x \right)}}{2} + \frac{\sin{\left(4 x \right)}}{8 \left(2 x + 2\right)}\right)}{2}\right) + \frac{\sin{\left(4 x \right)}}{32}$$

(sin(4*x)/(((2 + 2*x)*8)) + sin(2*x)/2 + x/2)/2 - x/16 + sin(4*x)/32

General simplification [src]

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

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

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

Rational denominator [src]

2048*sin(4*x) + (2048 + 2048*x)*sin(4*x) - 32*x*(128 + 128*x) + 512*x*(32 + 32*x) + 1024*(16 + 16*x)*sin(2*x)
-------------------------------------------------------------------------------------------------------------
                                               65536 + 65536*x

$$\frac{512 x \left(32 x + 32\right) - 32 x \left(128 x + 128\right) + 1024 \left(16 x + 16\right) \sin{\left(2 x \right)} + \left(2048 x + 2048\right) \sin{\left(4 x \right)} + 2048 \sin{\left(4 x \right)}}{65536 x + 65536}$$

(2048*sin(4*x) + (2048 + 2048*x)*sin(4*x) - 32*x*(128 + 128*x) + 512*x*(32 + 32*x) + 1024*(16 + 16*x)*sin(2*x))/(65536 + 65536*x)

Common denominator [src]

sin(2*x)   sin(4*x)   3*x    sin(4*x)
-------- + -------- + --- + ---------
   4          32       16   32 + 32*x

$$\frac{3 x}{16} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} + \frac{\sin{\left(4 x \right)}}{32 x + 32}$$

sin(2*x)/4 + sin(4*x)/32 + 3*x/16 + sin(4*x)/(32 + 32*x)

Powers [src]

        /   -2*I*x    2*I*x\     /   -4*I*x    4*I*x\     /   -4*I*x    4*I*x\
3*x   I*\- e       + e     /   I*\- e       + e     /   I*\- e       + e     /
--- - ---------------------- - ---------------------- - ----------------------
 16             8                        64                 4*(16 + 16*x)

$$\frac{3 x}{16} - \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{8} - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{64} - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{4 \left(16 x + 16\right)}$$

sin(2*x)   sin(4*x)   3*x      sin(4*x)  
-------- + -------- + --- + -------------
   4          32       16   2*(16 + 16*x)

$$\frac{3 x}{16} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

sin(2*x)/4 + sin(4*x)/32 + 3*x/16 + sin(4*x)/(2*(16 + 16*x))

Combinatorics [src]

                      2                                         
2*sin(4*x) + 6*x + 6*x  + 8*sin(2*x) + x*sin(4*x) + 8*x*sin(2*x)
----------------------------------------------------------------
                           32*(1 + x)

$$\frac{6 x^{2} + 8 x \sin{\left(2 x \right)} + x \sin{\left(4 x \right)} + 6 x + 8 \sin{\left(2 x \right)} + 2 \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$

(2*sin(4*x) + 6*x + 6*x^2 + 8*sin(2*x) + x*sin(4*x) + 8*x*sin(2*x))/(32*(1 + x))

Combining rational expressions [src]

(1 + x)*sin(4*x) + 6*x*(1 + x) + 8*(1 + x)*sin(2*x) + sin(4*x)
--------------------------------------------------------------
                          32*(1 + x)

$$\frac{6 x \left(x + 1\right) + 8 \left(x + 1\right) \sin{\left(2 x \right)} + \left(x + 1\right) \sin{\left(4 x \right)} + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$

((1 + x)*sin(4*x) + 6*x*(1 + x) + 8*(1 + x)*sin(2*x) + sin(4*x))/(32*(1 + x))

Numerical answer [src]

0.03125*sin(4*x) + 0.25*sin(2*x) + 0.1875*x + 0.5*sin(4*x)/(16.0 + 16.0*x)

0.03125*sin(4*x) + 0.25*sin(2*x) + 0.1875*x + 0.5*sin(4*x)/(16.0 + 16.0*x)

Expand expression [src]

         3                                    3                            
3*x   sin (x)*cos(x)   5*cos(x)*sin(x)   4*sin (x)*cos(x)   2*cos(x)*sin(x)
--- - -------------- + --------------- - ---------------- + ---------------
 16         4                 8             16 + 16*x          16 + 16*x

$$\frac{3 x}{16} - \frac{\sin^{3}{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{16 x + 16} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{16 x + 16}$$

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

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

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

Assemble expression [src]

sin(2*x)   sin(4*x)   3*x      sin(4*x)  
-------- + -------- + --- + -------------
   4          32       16   2*(16 + 16*x)

$$\frac{3 x}{16} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

sin(2*x)/4 + sin(4*x)/32 + 3*x/16 + sin(4*x)/(2*(16 + 16*x))

Trigonometric part [src]

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

$$\frac{3 x}{16} + \frac{\tan{\left(2 x \right)}}{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)} + \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{\tan{\left(2 x \right)}}{\left(16 x + 16\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$

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

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

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

$$\frac{3 x}{16} + \frac{\cot{\left(2 x \right)}}{16 \left(\cot^{2}{\left(2 x \right)} + 1\right)} + \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} + \frac{\cot{\left(2 x \right)}}{\left(16 x + 16\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$

   /      pi\      /      pi\            /      pi\
cos|2*x - --|   cos|4*x - --|         cos|4*x - --|
   \      2 /      \      2 /   3*x      \      2 /
------------- + ------------- + --- + -------------
      4               32         16   2*(16 + 16*x)

$$\frac{3 x}{16} + \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} + \frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{32} + \frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{2 \left(16 x + 16\right)}$$

    1             1        3*x             1           
---------- + ----------- + --- + ----------------------
4*csc(2*x)   32*csc(4*x)    16   2*(16 + 16*x)*csc(4*x)

$$\frac{3 x}{16} + \frac{1}{32 \csc{\left(4 x \right)}} + \frac{1}{4 \csc{\left(2 x \right)}} + \frac{1}{2 \left(16 x + 16\right) \csc{\left(4 x \right)}}$$

       1                 1           3*x                1             
--------------- + ---------------- + --- + ---------------------------
     /      pi\         /      pi\    16                    /      pi\
4*sec|2*x - --|   32*sec|4*x - --|         2*(16 + 16*x)*sec|4*x - --|
     \      2 /         \      2 /                          \      2 /

$$\frac{3 x}{16} + \frac{1}{32 \sec{\left(4 x - \frac{\pi}{2} \right)}} + \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \left(16 x + 16\right) \sec{\left(4 x - \frac{\pi}{2} \right)}}$$

sin(2*x)   sin(4*x)   3*x      sin(4*x)  
-------- + -------- + --- + -------------
   4          32       16   2*(16 + 16*x)

$$\frac{3 x}{16} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$

sin(2*x)/4 + sin(4*x)/32 + 3*x/16 + sin(4*x)/(2*(16 + 16*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-x/16+sin(4*x)/32

The solution

Least common denominator (sin(4x)/((2+2x)8)+sin(2x)/2+x/2)/2-x/16+sin(4*x)/32