Answer
-(2x + h)/($x^{4}$ + 2x³h + x²h²)
-(w + x)/x²w²
Work Step by Step
f(x) = 1/x²
f(x + h) = 1/(x + h)² = 1/(x² + 2xh + h²)
[f(x + h) - f(x)]/h = {[1/(x² + 2xh + h²)] - (1/x²)}/h =
= {[x² - (x² + 2xh + h²)]/[x²(x² + 2xh + h²)]}/h =
= [(-2hx - h²)/($x^{4}$ + 2x³h + x²h²)]/h =
= -(2x + h)/($x^{4}$ + 2x³h + x²h²)
f(w) = 1/w²
[f(w) - f(x)]/(w - x) = (1/w² - 1/x²)/(w - x) = [(x² - w²)/x²w²]/(w - x) =
= [(x + w)(x - w)/x²w²]/(w - x) = [-(w - x)(w + x)/x²w²]/(w - x) =
= -(w + x)/x²w²
