Basic Math Examples

$(4 g^{2} - 9) \div (2 g - 3)$

Step 1

Rewrite the division as a fraction.

$\frac{4 g^{2} - 9}{2 g - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4 g^{2}$ as ${(2 g)}^{2}$ .

$\frac{{(2 g)}^{2} - 9}{2 g - 3}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

$\frac{{(2 g)}^{2} - 3^{2}}{2 g - 3}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 g$ and $b = 3$ .

$\frac{(2 g + 3) (2 g - 3)}{2 g - 3}$

Step 3

Cancel the common factor of $2 g - 3$ .

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Step 3.1

Cancel the common factor.

$\frac{(2 g + 3) (2 g - 3)}{2 g - 3}$

Step 3.2

Divide $2 g + 3$ by $1$ .

$2 g + 3$