Mister Exam

Lang:

How to use it?
How do you in partial fractions?:
((z+2)/(2*z+4))+((2*z+1)/(3*z-4))
-(z^2+1)/(z-(-1-sqrt(3)*i)/2)^2+2*z/(z-(-1-sqrt(3)*i)/2)
2*(-1+4*x^2/(1+x^2))/(1+x^2)^2
2*x/(x^2-1)
Factor polynomial:
x^3-4*x
m^2-n^2-m+n
x^2-x^2
x^2-x-1
Least common denominator:
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
sqrt(m)/(m-16)-sqrt(m)/((4-sqrt(m))^2)
z/t-t/z
((z+p)/(2*(z-p)))-((z-p)/(2*(z+p)))-((p)/(z-p))
Factor squared:
y^4-y^2+10
y^4-y^2+1
y^4-9*y^2+8
y^4-y^2-1
Derivative of:
2*(-1+4*x^2/(1+x^2))/(1+x^2)^2
Identical expressions
two *(- one + four *x^ two /(one +x^ two))/(one +x^ two)^ two
2 multiply by ( minus 1 plus 4 multiply by x squared divide by (1 plus x squared )) divide by (1 plus x squared ) squared
two multiply by ( minus one plus four multiply by x to the power of two divide by (one plus x to the power of two)) divide by (one plus x to the power of two) to the power of two
2*(-1+4*x2/(1+x2))/(1+x2)2
2*-1+4*x2/1+x2/1+x22
2*(-1+4*x²/(1+x²))/(1+x²)²
2*(-1+4*x to the power of 2/(1+x to the power of 2))/(1+x to the power of 2) to the power of 2
2(-1+4x^2/(1+x^2))/(1+x^2)^2
2(-1+4x2/(1+x2))/(1+x2)2
2-1+4x2/1+x2/1+x22
2-1+4x^2/1+x^2/1+x^2^2
2*(-1+4*x^2 divide by (1+x^2)) divide by (1+x^2)^2
Similar expressions
2*(-1+4*x^2/(1+x^2))/(1-x^2)^2
2*(-1+4*x^2/(1-x^2))/(1+x^2)^2
2*(1+4*x^2/(1+x^2))/(1+x^2)^2
2*(-1-4*x^2/(1+x^2))/(1+x^2)^2

How do you 2(-1+4x^2/(1+x^2))/(1+x^2)^2 in partial fractions?

You have entered [src]

  /         2 \
  |      4*x  |
2*|-1 + ------|
  |          2|
  \     1 + x /
---------------
           2   
   /     2\    
   \1 + x /

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

(2*(-1 + (4*x^2)/(1 + x^2)))/(1 + x^2)^2

General simplification [src]

  /        2\
2*\-1 + 3*x /
-------------
          3  
  /     2\   
  \1 + x /

$$\frac{2 \left(3 x^{2} - 1\right)}{\left(x^{2} + 1\right)^{3}}$$

2*(-1 + 3*x^2)/(1 + x^2)^3

Fraction decomposition [src]

-8/(1 + x^2)^3 + 6/(1 + x^2)^2

$$\frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{8}{\left(x^{2} + 1\right)^{3}}$$

      8           6    
- --------- + ---------
          3           2
  /     2\    /     2\ 
  \1 + x /    \1 + x /

Assemble expression [src]

         2 
      8*x  
-2 + ------
          2
     1 + x 
-----------
         2 
 /     2\  
 \1 + x /

$$\frac{\frac{8 x^{2}}{x^{2} + 1} - 2}{\left(x^{2} + 1\right)^{2}}$$

(-2 + 8*x^2/(1 + x^2))/(1 + x^2)^2

Trigonometric part [src]

         2 
      8*x  
-2 + ------
          2
     1 + x 
-----------
         2 
 /     2\  
 \1 + x /

$$\frac{\frac{8 x^{2}}{x^{2} + 1} - 2}{\left(x^{2} + 1\right)^{2}}$$

(-2 + 8*x^2/(1 + x^2))/(1 + x^2)^2

Rational denominator [src]

        2
-2 + 6*x 
---------
        3
/     2\ 
\1 + x /

$$\frac{6 x^{2} - 2}{\left(x^{2} + 1\right)^{3}}$$

(-2 + 6*x^2)/(1 + x^2)^3

Common denominator [src]

             2      
     -2 + 6*x       
--------------------
     6      2      4
1 + x  + 3*x  + 3*x

$$\frac{6 x^{2} - 2}{x^{6} + 3 x^{4} + 3 x^{2} + 1}$$

(-2 + 6*x^2)/(1 + x^6 + 3*x^2 + 3*x^4)

Combining rational expressions [src]

  /        2\
2*\-1 + 3*x /
-------------
          3  
  /     2\   
  \1 + x /

$$\frac{2 \left(3 x^{2} - 1\right)}{\left(x^{2} + 1\right)^{3}}$$

2*(-1 + 3*x^2)/(1 + x^2)^3

Numerical answer [src]

(-2.0 + 8.0*x^2/(1.0 + x^2))/(1.0 + x^2)^2

(-2.0 + 8.0*x^2/(1.0 + x^2))/(1.0 + x^2)^2

Powers [src]

         2 
      8*x  
-2 + ------
          2
     1 + x 
-----------
         2 
 /     2\  
 \1 + x /

$$\frac{\frac{8 x^{2}}{x^{2} + 1} - 2}{\left(x^{2} + 1\right)^{2}}$$

(-2 + 8*x^2/(1 + x^2))/(1 + x^2)^2

Combinatorics [src]

  /        2\
2*\-1 + 3*x /
-------------
          3  
  /     2\   
  \1 + x /

$$\frac{2 \left(3 x^{2} - 1\right)}{\left(x^{2} + 1\right)^{3}}$$

2*(-1 + 3*x^2)/(1 + x^2)^3

How do you 2*(-1+4*x^2/(1+x^2))/(1+x^2)^2 in partial fractions?