Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2
(sin(2*x)/2+x)/2
(c*(v/k+1)+t)/((n+k)*(v/k+1)-k)
(a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))/(a-b)+(2*sqrt(b))/(sqrt(a)+sqrt(b))
Factor polynomial:
x^2-y^2+x-y
x^3+y^6
x^3*c^2-x^3*d^2
c^3+x^2+1-3*c^3+5
Factor squared:
y^4-y^2-8
-y^4+y^2-7
y^4-9*y^2+1
-y^2-4*y+3
How do you in partial fractions?:
z/(z+4)^2-z/z^2-16
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
(a+4)*a/2+(4*a+16)/(4*a^2+a^3)
((9*b)/(a-b))*((a^2-a*b)/(45*b))
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) plus 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) plus 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)*sin(2*x) + 8*x*(1 + x) + sin(4*x)
-------------------------------------------
                 32*(1 + x)

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

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

Powers [src]

x   sin(2*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))

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

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

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

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

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

Common denominator [src]

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

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

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

Combining rational expressions [src]

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

Combinatorics [src]

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

Trigonometric part [src]

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

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

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

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

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

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

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

Assemble expression [src]

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

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

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

Other calculators

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