Mister Exam

# Least common denominator exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2

An expression to simplify:

### The solution

You have entered [src]
   x            x
e        2*x*e
------ + ---------
2           2
1 - x    /     2\
\1 - x / 
$$\frac{2 x e^{x}}{\left(1 - x^{2}\right)^{2}} + \frac{e^{x}}{1 - x^{2}}$$
exp(x)/(1 - x^2) + ((2*x)*exp(x))/(1 - x^2)^2
General simplification [src]
/     2      \  x
\1 - x  + 2*x/*e
-----------------
2
/      2\
\-1 + x /    
$$\frac{\left(- x^{2} + 2 x + 1\right) e^{x}}{\left(x^{2} - 1\right)^{2}}$$
(1 - x^2 + 2*x)*exp(x)/(-1 + x^2)^2
Combinatorics [src]
 /      2      \  x
-\-1 + x  - 2*x/*e
--------------------
2         2
(1 + x) *(-1 + x)  
$$- \frac{\left(x^{2} - 2 x - 1\right) e^{x}}{\left(x - 1\right)^{2} \left(x + 1\right)^{2}}$$
-(-1 + x^2 - 2*x)*exp(x)/((1 + x)^2*(-1 + x)^2)
Rational denominator [src]
        2
/     2\   x       /     2\  x
\1 - x / *e  + 2*x*\1 - x /*e
------------------------------
3
/     2\
\1 - x /            
$$\frac{2 x \left(1 - x^{2}\right) e^{x} + \left(1 - x^{2}\right)^{2} e^{x}}{\left(1 - x^{2}\right)^{3}}$$
((1 - x^2)^2*exp(x) + 2*x*(1 - x^2)*exp(x))/(1 - x^2)^3
exp(x)/(1.0 - x^2) + 2.0*x*exp(x)/(1.0 - x^2)^2
exp(x)/(1.0 - x^2) + 2.0*x*exp(x)/(1.0 - x^2)^2
Common denominator [src]
 /   x    2  x        x\
-\- e  + x *e  - 2*x*e /
-------------------------
4      2
1 + x  - 2*x       
$$- \frac{x^{2} e^{x} - 2 x e^{x} - e^{x}}{x^{4} - 2 x^{2} + 1}$$
-(-exp(x) + x^2*exp(x) - 2*x*exp(x))/(1 + x^4 - 2*x^2)
Combining rational expressions [src]
/     2      \  x
\1 - x  + 2*x/*e
-----------------
2
/     2\
\1 - x /     
$$\frac{\left(- x^{2} + 2 x + 1\right) e^{x}}{\left(1 - x^{2}\right)^{2}}$$
(1 - x^2 + 2*x)*exp(x)/(1 - x^2)^2
Trigonometric part [src]
  cosh(x) + sinh(x)   2*x*(cosh(x) + sinh(x))
- ----------------- + -----------------------
2                        2
-1 + x                /      2\
\-1 + x /       
$$\frac{2 x \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x^{2} - 1\right)^{2}} - \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{2} - 1}$$
cosh(x) + sinh(x)   2*x*(cosh(x) + sinh(x))
----------------- + -----------------------
2                       2
1 - x                /     2\
\1 - x /        
$$\frac{2 x \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(1 - x^{2}\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{1 - x^{2}}$$
(cosh(x) + sinh(x))/(1 - x^2) + 2*x*(cosh(x) + sinh(x))/(1 - x^2)^2