Question

find the rational expression R whose numerator and denominator have degree 2 and leading coefficients of 1 such that (x^2 + 3x-10)/(x^2 -8x+15) * R = (x-2)/(x-3)

Answer 1

x^2+3x-10 = (x+5)(x-2)
x^2-8x+15 = (x-5)(x-3)

So, you want

(x+5)(x-2) / (x-5)(x-3) * R = (x-2)/(x-3)

So, you have

R = (x-2)/(x-3) * (x-5)(x-3) / (x+5)(x-2)
R = (x-5)/(x+5)

Answer 2

87