Precalculus Examples

$\frac{9 x^{2} - 16 y^{2}}{6 x^{2} - 8 x y}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{{(3 x)}^{2} - 16 y^{2}}{6 x^{2} - 8 x y}$

Step 1.2

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

$\frac{{(3 x)}^{2} - {(4 y)}^{2}}{6 x^{2} - 8 x y}$

Step 1.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 4 y$ .

$\frac{(3 x + 4 y) (3 x - (4 y))}{6 x^{2} - 8 x y}$

Step 1.4

Multiply $4$ by $- 1$ .

$\frac{(3 x + 4 y) (3 x - 4 y)}{6 x^{2} - 8 x y}$

Step 2

Simplify terms.

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Step 2.1

Factor $2 x$ out of $6 x^{2} - 8 x y$ .

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Step 2.1.1

Factor $2 x$ out of $6 x^{2}$ .

$\frac{(3 x + 4 y) (3 x - 4 y)}{2 x (3 x) - 8 x y}$

Step 2.1.2

Factor $2 x$ out of $- 8 x y$ .

$\frac{(3 x + 4 y) (3 x - 4 y)}{2 x (3 x) + 2 x (- 4 y)}$

Step 2.1.3

Factor $2 x$ out of $2 x (3 x) + 2 x (- 4 y)$ .

$\frac{(3 x + 4 y) (3 x - 4 y)}{2 x (3 x - 4 y)}$

Step 2.2

Cancel the common factor of $3 x - 4 y$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(3 x + 4 y) (3 x - 4 y)}{2 x (3 x - 4 y)}$

Step 2.2.2

Rewrite the expression.

$\frac{3 x + 4 y}{2 x}$