Partial fraction

Question

Express the following as partial fractions

(2x² + x - 5)/(x - 4)

I don't see any tutorial on YouTube with non quadratic functions as the denominator. Please help with this question.

Answer 1

quotient = 2x + 9 with a remainder of 31

Use long or synthetic division

(2x^2 +x -5)/(x-4) = 2x+9 + 31/(x-4)

4 |2 1 -5

8

2 9 36

31

also

(2x^2 +x -5)/(x-4) = 2x^2/(x-4) + x/(x-4) - 5/(x-4), breaking it up into 3 fractions