Pre-Algebra Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Multiply the numerator and denominator of the fraction by $x^{2}$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

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

Step 4

Simplify by cancelling.

Tap for more steps...

Step 4.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $x^{2}$ .

Tap for more steps...

Step 4.2.1

Move the leading negative in $- \frac{49}{x^{2}}$ into the numerator.

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Factor $x$ out of $x^{2} \cdot 1 + x \cdot 7$ .

Tap for more steps...

Step 5.1.1

Factor $x$ out of $x^{2} \cdot 1$ .

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

Step 5.1.2

Factor $x$ out of $x \cdot 7$ .

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

Step 5.1.3

Factor $x$ out of $x (x \cdot 1) + x (7)$ .

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

Step 5.2

Multiply $x$ by $1$ .

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

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Rewrite $x^{2} \cdot 1$ as ${(x \cdot 1)}^{2}$ .

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

Step 6.2

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

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

Step 6.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x \cdot 1$ and $b = 7$ .

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

Step 6.4

Simplify.

Tap for more steps...

Step 6.4.1

Multiply $x$ by $1$ .

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

Step 6.4.2

Multiply $x$ by $1$ .

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

Step 7

Cancel the common factor of $x + 7$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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