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Least common denominator:
sin(k*x+x/2)/2*sin(x/2)+cos(k*x+x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
sin(2*pi+x)+((3*pi)/2-x)+cos(x+pi/2)
x^4/4+x+2+x^4/4+x+2
Factor polynomial:
z^2-20*z+104
x^5+x^7
x1*x2+x1^2*x3^2+x2*x3
2*c^4-4*c^3+2*c
Factor squared:
-y^4-y^2+8
x^2-x*a+4*a^2
3*x^2+5*x-3
-y^2-4*y-3
How do you in partial fractions?:
((x*x-11*x+30)/(x*x-9*x+20))/((x*x-36)/(x*x-16))
((6*p/(2*p-5))*4)/(1+((6*p/(2*p-5))/p)+(6*p/(2*p-5))*4*((-5)/p))*(2-7/4*p)/(1-7/4*p*6)
2/x+(3*x-2)/(x+1)
(a^-2-a/a^-1-1)/(a^2+1)
Identical expressions
sin(k*x+x/ two)/ two *sin(x/ two)+cos(k*x+x)
sinus of (k multiply by x plus x divide by 2) divide by 2 multiply by sinus of (x divide by 2) plus co sinus of e of (k multiply by x plus x)
sinus of (k multiply by x plus x divide by two) divide by two multiply by sinus of (x divide by two) plus co sinus of e of (k multiply by x plus x)
sin(kx+x/2)/2sin(x/2)+cos(kx+x)
sinkx+x/2/2sinx/2+coskx+x
sin(k*x+x divide by 2) divide by 2*sin(x divide by 2)+cos(k*x+x)
Similar expressions
sin(k*x-x/2)/2*sin(x/2)+cos(k*x+x)
sin(k*x+x/2)/2*sin(x/2)+cos(k*x-x)
sin(k*x+x/2)/2*sin(x/2)-cos(k*x+x)

Expression simplification/ Least common denominator/ sin(k*x+x/2)/2*sin(x/2)+cos(k*x+x)

Least common denominator sin(kx+x/2)/2sin(x/2)+cos(k*x+x)

The solution

You have entered [src]

   /      x\                      
sin|k*x + -|                      
   \      2/    /x\               
------------*sin|-| + cos(k*x + x)
     2          \2/

$$\frac{\sin{\left(k x + \frac{x}{2} \right)}}{2} \sin{\left(\frac{x}{2} \right)} + \cos{\left(k x + x \right)}$$

(sin(k*x + x/2)/2)*sin(x/2) + cos(k*x + x)

General simplification [src]

cos(k*x)   3*cos(x*(1 + k))
-------- + ----------------
   4              4

$$\frac{\cos{\left(k x \right)}}{4} + \frac{3 \cos{\left(x \left(k + 1\right) \right)}}{4}$$

cos(k*x)/4 + 3*cos(x*(1 + k))/4

Rational denominator [src]

                    /x\    /      x\
2*cos(x + k*x) + sin|-|*sin|k*x + -|
                    \2/    \      2/
------------------------------------
                 2

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(k x + \frac{x}{2} \right)} + 2 \cos{\left(k x + x \right)}}{2}$$

(2*cos(x + k*x) + sin(x/2)*sin(k*x + x/2))/2

Assemble expression [src]

   /x\    /      x\               
sin|-|*sin|k*x + -|               
   \2/    \      2/               
------------------- + cos(k*x + x)
         2

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(k x + \frac{x}{2} \right)}}{2} + \cos{\left(k x + x \right)}$$

sin(x/2)*sin(k*x + x/2)/2 + cos(k*x + x)

Numerical answer [src]

0.5*sin(x/2)*sin(k*x + x/2) + cos(k*x + x)

0.5*sin(x/2)*sin(k*x + x/2) + cos(k*x + x)

Combining rational expressions [src]

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

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{x \left(2 k + 1\right)}{2} \right)} + 2 \cos{\left(x \left(k + 1\right) \right)}}{2}$$

(2*cos(x*(1 + k)) + sin(x/2)*sin(x*(1 + 2*k)/2))/2

Combinatorics [src]

   /x\    /x      \               
sin|-|*sin|- + k*x|               
   \2/    \2      /               
------------------- + cos(x + k*x)
         2

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(k x + \frac{x}{2} \right)}}{2} + \cos{\left(k x + x \right)}$$

sin(x/2)*sin(x/2 + k*x)/2 + cos(x + k*x)

Expand expression [src]

                     2/x\                                 /x\    /x\         
                  sin |-|*cos(k*x)                     cos|-|*sin|-|*sin(k*x)
                      \2/                                 \2/    \2/         
cos(x)*cos(k*x) + ---------------- - sin(x)*sin(k*x) + ----------------------
                         2                                       2

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

cos(x)*cos(k*x) + sin(x/2)^2*cos(k*x)/2 - sin(x)*sin(k*x) + cos(x/2)*sin(x/2)*sin(k*x)/2

Powers [src]

                               /     /  x      \      /x      \\ /   -I*x     I*x\
                               |   I*|- - - k*x|    I*|- + k*x|| |   -----    ---|
 I*(x + k*x)    I*(-x - k*x)   |     \  2      /      \2      /| |     2       2 |
e              e               \- e              + e           /*\- e      + e   /
------------ + ------------- - ---------------------------------------------------
     2               2                                  8

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

   /x\    /x      \               
sin|-|*sin|- + k*x|               
   \2/    \2      /               
------------------- + cos(x + k*x)
         2

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(k x + \frac{x}{2} \right)}}{2} + \cos{\left(k x + x \right)}$$

sin(x/2)*sin(x/2 + k*x)/2 + cos(x + k*x)

Common denominator [src]

   /x\    /x      \               
sin|-|*sin|- + k*x|               
   \2/    \2      /               
------------------- + cos(x + k*x)
         2

$$\frac{\sin{\left(\frac{x}{2} \right)} \sin{\left(k x + \frac{x}{2} \right)}}{2} + \cos{\left(k x + x \right)}$$

sin(x/2)*sin(x/2 + k*x)/2 + cos(x + k*x)

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Identical expressions

Similar expressions

Least common denominator sin(k*x+x/2)/2*sin(x/2)+cos(k*x+x)

The solution

Least common denominator sin(kx+x/2)/2sin(x/2)+cos(k*x+x)