Simpify into two partial fractions:2x-3/ (x^2 -5x -50)

We have to find the partial fractions of 2x-3/ (x^2 -5x
-50)

2x-3/ (x^2 -5x
-50)

=> 2x - 3 / (x^2 - 10x + 5x -
50)

=> 2x - 3 / (x(x - 10) + 5(x -
10))

=> 2x - 3 / (x + 5)(x -
10)

=> A / (x + 5) + B/(x -
10)

=> Ax - 10A + Bx + 5B = 2x -
3

=> A + B  = 2 and 10A - 5B =
3

=> 10A + 10B = 20 and 10A - 5B =
3

subtract the two
equations

=> 15B =
17

=> B = 17/15

A =
13/15

The partial fractions are 13/15*(x + 5)
+ 17/15*(x - 10)