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Expression simplification/ Least common denominator/ ((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

Least common denominator ((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

An expression to simplify:

The solution

You have entered [src] 
sin(4*x)                        sin(4*x)                     
-------- + 2*x                  -------- + 2*x               
   2             sin(2*x)   x      2             sin(2*x)   x
-------------- + -------- + -   -------------- - -------- + -
      8             2       2         8             2       2
----------------------------- - -----------------------------
              2                               2
$$- \frac{\frac{x}{2} + \left(\frac{2 x + \frac{\sin{\left(4 x \right)}}{2}}{8} - \frac{\sin{\left(2 x \right)}}{2}\right)}{2} + \frac{\frac{x}{2} + \left(\frac{2 x + \frac{\sin{\left(4 x \right)}}{2}}{8} + \frac{\sin{\left(2 x \right)}}{2}\right)}{2}$$ 
((sin(4*x)/2 + 2*x)/8 + sin(2*x)/2 + x/2)/2 - ((sin(4*x)/2 + 2*x)/8 - sin(2*x)/2 + x/2)/2
General simplification [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Fraction decomposition [src] 
sin(2*x)/2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)
--------
   2
Rational denominator [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Combining rational expressions [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Powers [src] 
   /   -2*I*x    2*I*x\ 
-I*\- e       + e     / 
------------------------
           4
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{4}$$ 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Numerical answer [src] 
0.5*sin(2*x)
0.5*sin(2*x)
Combinatorics [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Common denominator [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Expand expression [src] 
cos(x)*sin(x)
$$\sin{\left(x \right)} \cos{\left(x \right)}$$ 
cos(x)*sin(x)
Assemble expression [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
sin(2*x)/2
Trigonometric part [src] 
sin(2*x)
--------
   2
$$\frac{\sin{\left(2 x \right)}}{2}$$ 
       1       
---------------
     /      pi\
2*sec|2*x - --|
     \      2 /
$$\frac{1}{2 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$ 
    1     
----------
2*csc(2*x)
$$\frac{1}{2 \csc{\left(2 x \right)}}$$ 
   tan(x)  
-----------
       2   
1 + tan (x)
$$\frac{\tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}$$ 
   cot(x)  
-----------
       2   
1 + cot (x)
$$\frac{\cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}$$ 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
      2
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{2}$$ 
cos(2*x - pi/2)/2
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