Mister Exam

Lang:

Other calculators

How to use it?
How do you in partial fractions?:
(5a^2-20)/(5a^2-22a+8)*(4-a)/(a-2)
atan(((6*sin(x))/(1+cos(x))+2)/2^(5/2))/sqrt(2)
atan(((2*sin(2*x))/(1+cos(2*x))+2)/2^(5/2))/2^(3/2)
atan((2*x+4)/(2*sqrt(3)))/sqrt(3)
Factor polynomial:
x^4-3*x^2*y
x^4-2*x^3*y-8*x^2*y^2-6*x*y^3-y^4
x^4-2*x^3*y-4*x^2*y^2+5*x*y^3-6*y^4
x^4+2*x^3+4*x-3*x^2/2
Least common denominator:
-log(((4*sin(x))/(1+cos(x))-sqrt(17)+1)/(1+sqrt(17)+(4*sin(x))/(1+cos(x))))/sqrt(17)
i1-((e-z1*i1)/(z2))-((z2*i2)/(z3+z4))
-g/2*(p/l)^2+(v-o*(v-b)/l^2)*(p/l)
exp(x)/(-4*tan(x)-2*sin(x))^4+(16+8*cos(x)+16*tan(x)^2)*exp(x)/(-4*tan(x)-2*sin(x))^5
Factor squared:
y^2+2*y*b-12*b^2
-y^2+2*y-9
y^2-15*y-2
-y^2+15*y-10
Identical expressions
((two *x^ two + four)/(x^ four - seventy-seven *x^ two + four))^ two +((- eighteen *x)/(x^ four - seventy-seven *x^ two + four))^ two
((2 multiply by x squared plus 4) divide by (x to the power of 4 minus 77 multiply by x squared plus 4)) squared plus (( minus 18 multiply by x) divide by (x to the power of 4 minus 77 multiply by x squared plus 4)) squared
((two multiply by x to the power of two plus four) divide by (x to the power of four minus seventy minus seven multiply by x to the power of two plus four)) to the power of two plus (( minus eighteen multiply by x) divide by (x to the power of four minus seventy minus seven multiply by x to the power of two plus four)) to the power of two
((2*x2+4)/(x4-77*x2+4))2+((-18*x)/(x4-77*x2+4))2
2*x2+4/x4-77*x2+42+-18*x/x4-77*x2+42
((2*x²+4)/(x⁴-77*x²+4))²+((-18*x)/(x⁴-77*x²+4))²
((2*x to the power of 2+4)/(x to the power of 4-77*x to the power of 2+4)) to the power of 2+((-18*x)/(x to the power of 4-77*x to the power of 2+4)) to the power of 2
((2x^2+4)/(x^4-77x^2+4))^2+((-18x)/(x^4-77x^2+4))^2
((2x2+4)/(x4-77x2+4))2+((-18x)/(x4-77x2+4))2
2x2+4/x4-77x2+42+-18x/x4-77x2+42
2x^2+4/x^4-77x^2+4^2+-18x/x^4-77x^2+4^2
((2*x^2+4) divide by (x^4-77*x^2+4))^2+((-18*x) divide by (x^4-77*x^2+4))^2
Similar expressions
((2*x^2+4)/(x^4+77*x^2+4))^2+((-18*x)/(x^4-77*x^2+4))^2
((2*x^2+4)/(x^4-77*x^2+4))^2-((-18*x)/(x^4-77*x^2+4))^2
((2*x^2+4)/(x^4-77*x^2+4))^2+((-18*x)/(x^4+77*x^2+4))^2
((2*x^2+4)/(x^4-77*x^2+4))^2+((18*x)/(x^4-77*x^2+4))^2
((2*x^2+4)/(x^4-77*x^2-4))^2+((-18*x)/(x^4-77*x^2+4))^2
((2*x^2+4)/(x^4-77*x^2+4))^2+((-18*x)/(x^4-77*x^2-4))^2
((2*x^2-4)/(x^4-77*x^2+4))^2+((-18*x)/(x^4-77*x^2+4))^2

Expression simplification/ Fraction Decomposition into the simple/ ((2*x^2+4)/(x^4-77*x^2+4))^2+((-18*x)/(x^4-77*x^2+4))^2

How do you ((2x^2+4)/(x^4-77x^2+4))^2+((-18x)/(x^4-77x^2+4))^2 in partial fractions?

The solution

You have entered [src]

                2                    
/      2       \                    2
|   2*x  + 4   |    /    -18*x     \ 
|--------------|  + |--------------| 
| 4       2    |    | 4       2    | 
\x  - 77*x  + 4/    \x  - 77*x  + 4/

$$\left(\frac{\left(-1\right) 18 x}{\left(x^{4} - 77 x^{2}\right) + 4}\right)^{2} + \left(\frac{2 x^{2} + 4}{\left(x^{4} - 77 x^{2}\right) + 4}\right)^{2}$$

((2*x^2 + 4)/(x^4 - 77*x^2 + 4))^2 + ((-18*x)/(x^4 - 77*x^2 + 4))^2

Fraction decomposition [src]

2/(2 + x^2 - 9*x)^2 + 2/(2 + x^2 + 9*x)^2

$$\frac{2}{\left(x^{2} + 9 x + 2\right)^{2}} + \frac{2}{\left(x^{2} - 9 x + 2\right)^{2}}$$

       2                 2       
--------------- + ---------------
              2                 2
/     2      \    /     2      \ 
\2 + x  - 9*x/    \2 + x  + 9*x/

General simplification [src]

  /        2        \
  |/     2\        2|
4*\\2 + x /  + 81*x /
---------------------
                  2  
  /     4       2\   
  \4 + x  - 77*x /

$$\frac{4 \left(81 x^{2} + \left(x^{2} + 2\right)^{2}\right)}{\left(x^{4} - 77 x^{2} + 4\right)^{2}}$$

4*((2 + x^2)^2 + 81*x^2)/(4 + x^4 - 77*x^2)^2

Numerical answer [src]

0.0026986001011975*(1 + 0.5*x^2)^2/(0.051948051948052 - x^2 + 0.012987012987013*x^4)^2 + 0.0546466520492494*x^2/(0.051948051948052 - x^2 + 0.012987012987013*x^4)^2

0.0026986001011975*(1 + 0.5*x^2)^2/(0.051948051948052 - x^2 + 0.012987012987013*x^4)^2 + 0.0546466520492494*x^2/(0.051948051948052 - x^2 + 0.012987012987013*x^4)^2

Assemble expression [src]

             2                       
   /       2\                  2     
   \4 + 2*x /             324*x      
----------------- + -----------------
                2                   2
/     4       2\    /     4       2\ 
\4 + x  - 77*x /    \4 + x  - 77*x /

$$\frac{324 x^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}} + \frac{\left(2 x^{2} + 4\right)^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}}$$

(4 + 2*x^2)^2/(4 + x^4 - 77*x^2)^2 + 324*x^2/(4 + x^4 - 77*x^2)^2

Common denominator [src]

                 4        2        
         16 + 4*x  + 340*x         
-----------------------------------
      8        2        6         4
16 + x  - 616*x  - 154*x  + 5937*x

$$\frac{4 x^{4} + 340 x^{2} + 16}{x^{8} - 154 x^{6} + 5937 x^{4} - 616 x^{2} + 16}$$

(16 + 4*x^4 + 340*x^2)/(16 + x^8 - 616*x^2 - 154*x^6 + 5937*x^4)

Rational denominator [src]

          2         
/       2\         2
\4 + 2*x /  + 324*x 
--------------------
                 2  
 /     4       2\   
 \4 + x  - 77*x /

$$\frac{324 x^{2} + \left(2 x^{2} + 4\right)^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}}$$

((4 + 2*x^2)^2 + 324*x^2)/(4 + x^4 - 77*x^2)^2

Expand expression [src]

             2                       
   /   2    \                  2     
   \2*x  + 4/             324*x      
----------------- + -----------------
                2                   2
/ 4       2    \    / 4       2    \ 
\x  - 77*x  + 4/    \x  - 77*x  + 4/

$$\frac{324 x^{2}}{\left(\left(x^{4} - 77 x^{2}\right) + 4\right)^{2}} + \frac{\left(2 x^{2} + 4\right)^{2}}{\left(\left(x^{4} - 77 x^{2}\right) + 4\right)^{2}}$$

(2*x^2 + 4)^2/(x^4 - 77*x^2 + 4)^2 + (324*x^2)/(x^4 - 77*x^2 + 4)^2

Combinatorics [src]

         /     4       2\      
       4*\4 + x  + 85*x /      
-------------------------------
              2               2
/     2      \  /     2      \ 
\2 + x  - 9*x/ *\2 + x  + 9*x/

$$\frac{4 \left(x^{4} + 85 x^{2} + 4\right)}{\left(x^{2} - 9 x + 2\right)^{2} \left(x^{2} + 9 x + 2\right)^{2}}$$

4*(4 + x^4 + 85*x^2)/((2 + x^2 - 9*x)^2*(2 + x^2 + 9*x)^2)

Trigonometric part [src]

             2                       
   /       2\                  2     
   \4 + 2*x /             324*x      
----------------- + -----------------
                2                   2
/     4       2\    /     4       2\ 
\4 + x  - 77*x /    \4 + x  - 77*x /

$$\frac{324 x^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}} + \frac{\left(2 x^{2} + 4\right)^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}}$$

(4 + 2*x^2)^2/(4 + x^4 - 77*x^2)^2 + 324*x^2/(4 + x^4 - 77*x^2)^2

Combining rational expressions [src]

  /        2        \
  |/     2\        2|
4*\\2 + x /  + 81*x /
---------------------
                    2
 /     2 /       2\\ 
 \4 + x *\-77 + x //

$$\frac{4 \left(81 x^{2} + \left(x^{2} + 2\right)^{2}\right)}{\left(x^{2} \left(x^{2} - 77\right) + 4\right)^{2}}$$

4*((2 + x^2)^2 + 81*x^2)/(4 + x^2*(-77 + x^2))^2

Powers [src]

             2                       
   /       2\                  2     
   \4 + 2*x /             324*x      
----------------- + -----------------
                2                   2
/     4       2\    /     4       2\ 
\4 + x  - 77*x /    \4 + x  - 77*x /

$$\frac{324 x^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}} + \frac{\left(2 x^{2} + 4\right)^{2}}{\left(x^{4} - 77 x^{2} + 4\right)^{2}}$$

(4 + 2*x^2)^2/(4 + x^4 - 77*x^2)^2 + 324*x^2/(4 + x^4 - 77*x^2)^2

Other calculators

How to use it?

Identical expressions

Similar expressions

How do you ((2*x^2+4)/(x^4-77*x^2+4))^2+((-18*x)/(x^4-77*x^2+4))^2 in partial fractions?

The solution

How do you ((2x^2+4)/(x^4-77x^2+4))^2+((-18x)/(x^4-77x^2+4))^2 in partial fractions?