Algebra Examples

$\frac{{(x + 7)}^{2}}{49 - x^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $49$ as $7^{2}$ .

$\frac{{(x + 7)}^{2}}{7^{2} - x^{2}}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7$ and $b = x$ .

$\frac{{(x + 7)}^{2}}{(7 + x) (7 - x)}$

Step 2

Cancel the common factor of ${(x + 7)}^{2}$ and $7 + x$ .

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Step 2.1

Reorder terms.

$\frac{{(x + 7)}^{2}}{(x + 7) (7 - x)}$

Step 2.2

Factor $x + 7$ out of ${(x + 7)}^{2}$ .

$\frac{(x + 7) (x + 7)}{(x + 7) (7 - x)}$

Step 2.3

Cancel the common factors.

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Step 2.3.1

Cancel the common factor.

$\frac{(x + 7) (x + 7)}{(x + 7) (7 - x)}$

Step 2.3.2

Rewrite the expression.

$\frac{x + 7}{7 - x}$