Home > Algebra calculators > Partial Fractions calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
Find Partial Fractions (5x-4)/(x^2-x-2)

Your problem `->` Partial Fractions (5x-4)/(x^2-x-2)

1. Factors the denominator

2. Partial fractions for each factors
`:. (5x-4)/((x+1)(x-2))=A/(x+1)+B/(x-2)`

3. Multiply through by the common denominator of `(x+1)(x-2)`

`:. 5x-4=A(x-2)+B(x+1)`

`:. 5x-4=Ax-2A+Bx+B`

4. Group the `x`-terms and the constant terms

`:. 5x-4=(A+B)x+(-2A+B)`

5. Coefficients of the two polynomials must be equal, so we get equations


Solution of equations using Elimination method

Total Equations are `2`

`A+B=5 -> (1)`

`-2A+B=-4 -> (2)`

Select the equations `(1)` and `(2)`, and eliminate the variable `B`.

`A+B=5`` xx 1->````A``+``B``=``5```
`-2A+B=-4`` xx 1->``-``2A``+``B``=``-4```

```3A``=``9`` -> (3)`

Now use back substitution method
From (3)



From (1)




Solution using Elimination method.
`A = 3,B = 2`

After solving these equations, we get

Substitute these values in the original fractions

Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me

Share with your friends, if solutions are helpful to you.
Copyright © 2019. All rights reserved. Terms, Privacy

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more