Mister Exam

# Least common denominator (sin(2*x)/2+x)/2

An expression to simplify:

### The solution

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