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Least common denominator:
4*x^(3/2)/3+2*sqrt(x)+x^5/5+e^(5*x^3+1)/15
z*((-z)*log(x)/c+z*log(y)/c)
(z*z-1/2*z)/(z*z-z+1)*z/(z-1/2)
-x^2/(x-2)^2+2*x/(x-2)
Factor polynomial:
x^2+3
x^4-x
x*y^3-x^3*y^2
x^2-1
Factor squared:
y^4+y^2+2
y^4+y^2-15
y^4-y^2-5
-y^4+8*y^2-8
How do you in partial fractions?:
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
(5x^2+9x-2)/(x^2-5x-14)
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
1/(2*sqrt(x))
Identical expressions
((sin(four *x)/ two + two *x)/ eight +sin(two *x)/ two +x/ two)/ two -(two *x-sin(four *x)/ two)/ sixteen
(( sinus of (4 multiply by x) divide by 2 plus 2 multiply by x) divide by 8 plus sinus of (2 multiply by x) divide by 2 plus x divide by 2) divide by 2 minus (2 multiply by x minus sinus of (4 multiply by x) divide by 2) divide by 16
(( sinus of (four multiply by x) divide by two plus two multiply by x) divide by eight plus sinus of (two multiply by x) divide by two plus x divide by two) divide by two minus (two multiply by x minus sinus of (four multiply by x) divide by two) divide by sixteen
((sin(4x)/2+2x)/8+sin(2x)/2+x/2)/2-(2x-sin(4x)/2)/16
sin4x/2+2x/8+sin2x/2+x/2/2-2x-sin4x/2/16
((sin(4*x) divide by 2+2*x) divide by 8+sin(2*x) divide by 2+x divide by 2) divide by 2-(2*x-sin(4*x) divide by 2) divide by 16
Similar expressions
((sin(4*x)/2+2*x)/8+sin(2*x)/2+x/2)/2-(2*x+sin(4*x)/2)/16
((sin(4*x)/2-2*x)/8+sin(2*x)/2+x/2)/2-(2*x-sin(4*x)/2)/16
((sin(4*x)/2+2*x)/8-sin(2*x)/2+x/2)/2-(2*x-sin(4*x)/2)/16
((sin(4*x)/2+2*x)/8+sin(2*x)/2+x/2)/2+(2*x-sin(4*x)/2)/16
((sin(4*x)/2+2*x)/8+sin(2*x)/2-x/2)/2-(2*x-sin(4*x)/2)/16

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

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

The solution

You have entered [src]

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

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

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

General simplification [src]

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

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

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

Rational denominator [src]

256*sin(4*x) + 1024*x + 1024*sin(2*x)
-------------------------------------
                 4096

$$\frac{1024 x + 1024 \sin{\left(2 x \right)} + 256 \sin{\left(4 x \right)}}{4096}$$

(256*sin(4*x) + 1024*x + 1024*sin(2*x))/4096

Numerical answer [src]

0.0625*sin(4*x) + 0.25*x + 0.25*sin(2*x)

0.0625*sin(4*x) + 0.25*x + 0.25*sin(2*x)

Common denominator [src]

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

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

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

Powers [src]

      /   -2*I*x    2*I*x\     /   -4*I*x    4*I*x\
x   I*\- e       + e     /   I*\- e       + e     /
- - ---------------------- - ----------------------
4             8                        32

$$\frac{x}{4} - \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{8} - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{32}$$

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

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

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

Combinatorics [src]

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

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

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

Combining rational expressions [src]

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

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

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

Expand expression [src]

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

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

x/4 - sin(x)^3*cos(x)/2 + 3*cos(x)*sin(x)/4

Assemble expression [src]

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

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

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

Trigonometric part [src]

x        tan(x)            tan(2*x)    
- + --------------- + -----------------
4     /       2   \     /       2     \
    2*\1 + tan (x)/   8*\1 + tan (2*x)/

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

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

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

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

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

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

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

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

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

x        cot(x)            cot(2*x)    
- + --------------- + -----------------
4     /       2   \     /       2     \
    2*\1 + cot (x)/   8*\1 + cot (2*x)/

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

x/4 + cot(x)/(2*(1 + cot(x)^2)) + cot(2*x)/(8*(1 + cot(2*x)^2))

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Identical expressions

Similar expressions

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

The solution

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