Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

Step 2.2

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 $b = 1$ .

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

Step 3

Simplify terms.

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Step 3.1

Factor $49$ out of $49 x + 49$ .

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Step 3.1.1

Factor $49$ out of $49 x$ .

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

Step 3.1.2

Factor $49$ out of $49$ .

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

Step 3.1.3

Factor $49$ out of $49 (x) + 49 (1)$ .

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

Step 3.2

Cancel the common factor of $x - 1$ .

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Step 3.2.1

Factor $x - 1$ out of $(x + 1) (x - 1)$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x + 1}{49 (x + 1)} \cdot 7$

Step 3.3

Cancel the common factor of $7$ .

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Step 3.3.1

Factor $7$ out of $49 (x + 1)$ .

$\frac{x + 1}{7 (7 (x + 1))} \cdot 7$

Step 3.3.2

Cancel the common factor.

$\frac{x + 1}{7 (7 (x + 1))} \cdot 7$

Step 3.3.3

Rewrite the expression.

$\frac{x + 1}{7 (x + 1)}$

Step 3.4

Cancel the common factor of $x + 1$ .

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Step 3.4.1

Cancel the common factor.

$\frac{x + 1}{7 (x + 1)}$

Step 3.4.2

Rewrite the expression.

$\frac{1}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$