Question

Perform the operation and combine to one fraction.
start fraction, 3, divided by, x, plus, 8, end fraction, minus, start fraction, x, plus, 2, divided by, x, squared, plus, 3, x, minus, 40, end fraction
x+8
3
​
−
x
2
+3x−40
x+2

Answer 1

Factor the quadratic: x^2+3x−40 = (x+8)(x−5).
Put over common denominator and combine:

3/(x+8) − (x+2)/((x+8)(x−5))
= [3(x−5) − (x+2)]/((x+8)(x−5))
= (2x − 17)/((x+8)(x−5)).

Domain: x ≠ −8, 5.