Answer:
[tex]\frac{1}{(x-3)(x-2)}[/tex]
Step-by-step 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
[tex]\frac{x+2}{(x-3)(x+3)}[/tex] × [tex]\frac{x+3}{(x-2)(x+2)}[/tex]
Cancel the factors (x + 3) and (x + 2) from the numerators/denominators of both fractions leaving
[tex]\frac{1}{(x-3)(x-2)}[/tex]
