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Problem: Partial Fraction (5x-4)/(x^2-x-2) [ Calculator, Method and examples ]

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

1. Factors the denominator

2. Partial fraction 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 fraction

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