Question

Reduce each of the following rational expressions to its lowest form.

(i) (x² - 1)/(x² + x)

(ii) (x² - 11x + 18)/(x² - 4x + 4)

(iii) (9x² + 81x)/(x³ + 8x² - 9x)

(iv) (p² - 3p - 40)/(2p³ - 24p² + 64p)

Answer 1

(i) (x² - 1)/(x² + x) = (x + 1)(x - 1)/x(x + 1) = (x - 1)/x

(ii) (x² - 11x + 18)/(x² - 4x + 4) = (x - 2)(x - 9)/(x - 2)(x - 2) = (x - 9)/(x - 2)

(iii) (9x² + 81x)/(x³ + 8x² - 9x) = 9x(x + 9)/x(x² + 8x - 9) = 9(x + 9)/(x + 9)(x - 1)

= 9/(x - 1)

(iv) (p² - 3p - 40)/(2p³ - 24p² + 64p)