Question

x%20%2B%203%7D%7B%20%7Bx%7D%5E%7B2%7D%20-%204%20%7D%20" id="TexFormula1" title=" \frac{x + 2}{ {x}^{2} - 9 } \times \frac{x + 3}{ {x}^{2} - 4 } " alt=" \frac{x + 2}{ {x}^{2} - 9 } \times \frac{x + 3}{ {x}^{2} - 4 } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$\frac{1}{(x-3)(x-2)}$

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

$\frac{x+2}{(x-3)(x+3)}$ × $\frac{x+3}{(x-2)(x+2)}$

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

$\frac{1}{(x-3)(x-2)}$