Factorize the expression and divide them as directed:
$(9 x^{2} - 4) \div (3 x + 2)$

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Solution

Step 1: Factorize the expression
$9 x^{2} - 4 [∴ a^{2} - b^{2} = (a + b) (a - b)]$
$= (3 x)^{2} - 2^{2}$
$= (3 x - 2) (3 x + 2)$

Step 2: Perform division of given expression
$\frac{9 x^{2} - 4}{3 x + 2} = \frac{(3 x - 2) (3 x + 2)}{3 x + 2}$
$= 3 x - 2$
$∴ (9 x^{2} - 4) \div (3 x + 2) = 3 x - 2.$

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