Basic Math Examples

$(x^{2} - 49) \div \frac{(x - 1) (x + 7)}{x^{2} + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(x^{2} - 49) \frac{x^{2} + 1}{(x - 1) (x + 7)}$

Step 2

Multiply $x^{2} - 49$ by $\frac{x^{2} + 1}{(x - 1) (x + 7)}$ .

$\frac{(x^{2} - 49) (x^{2} + 1)}{(x - 1) (x + 7)}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{(x^{2} - 7^{2}) (x^{2} + 1)}{(x - 1) (x + 7)}$

Step 3.2

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

$\frac{(x + 7) (x - 7) (x^{2} + 1)}{(x - 1) (x + 7)}$

Step 4

Cancel the common factor of $x + 7$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 7) (x - 7) (x^{2} + 1)}{(x - 1) (x + 7)}$

Step 4.2

Rewrite the expression.

$\frac{(x - 7) (x^{2} + 1)}{x - 1}$