\frac{x + 2}{ {x}^(2) - 9 } * \frac{x + 3}{ {x}^(2) - 4 }

Question

asked Nov 11, 2020 208k views

1 Answer

Irwinb · Answer 1 · 2020-11-15T16:14:21+0000

Answer:

(1)/((x-3)(x-2))

Explanation:

Factorise the denominators of both fractions

x² - 9 and x² - 4 are both differences of squares and factor as

x² - 9 = (x - 3)(x + 3) and x² - 4 = (x - 2)(x + 2), thus express as

(x+2)/((x-3)(x+3)) ×
(x+3)/((x-2)(x+2))

Cancel the factors (x + 3) and (x + 2) from the numerators/denominators of both fractions leaving

(1)/((x-3)(x-2))