# How do you divide \frac { ( x + 1) } { 4} \div \frac { x } { 4} ?

Aug 22, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

$\frac{\frac{x + 1}{4}}{\frac{x}{4}}$

Now, we can use this rule for dividing fractions to divide the expression in the problem:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{\left(x + 1\right)}}{\textcolor{b l u e}{4}}}{\frac{\textcolor{g r e e n}{x}}{\textcolor{p u r p \le}{4}}} \implies \frac{\textcolor{red}{\left(x + 1\right)} \times \textcolor{p u r p \le}{4}}{\textcolor{b l u e}{4} \times \textcolor{g r e e n}{x}} \implies \frac{\textcolor{red}{\left(x + 1\right)} \times \cancel{\textcolor{p u r p \le}{4}}}{\cancel{\textcolor{b l u e}{4}} \times \textcolor{g r e e n}{x}} \implies$

$\frac{x + 1}{x}$

Or

$\frac{x}{x} + \frac{1}{x} \implies$

$1 + \frac{1}{x}$

Aug 22, 2017

$\frac{x + 1}{x}$

#### Explanation:

$\frac{x + 1}{4} \div \frac{x}{4}$

Dividing is the same as multiplying by the reciprocal.

$\frac{x + 1}{\cancel{4}} \times \frac{\cancel{4}}{x} \text{ } \leftarrow$ cancel

$= \frac{x + 1}{x}$

This cannot be simplified further.