# How do you simplify (4x+16)/x div (x+4)?

Mar 21, 2018

$\frac{4}{x}$

#### Explanation:

This is the same as $\frac{4 x + 16}{x} \times \frac{1}{x + 4}$ giving

$\frac{4 x + 16}{x \left(x + 4\right)}$

Factor out 4 from the top giving:

$\frac{4 \left(x + 4\right)}{x \left(x + 4\right)} \textcolor{w h i t e}{\text{d") ->color(white)("d}} \frac{4}{x} \times \frac{x + 4}{x + 4}$

But $\frac{x + 4}{x + 4} = 1$ giving

$\textcolor{w h i t e}{\text{ddddddddd") -> color(white)("d")4/x color(white)("d") xx color(white)("d}} 1 = \frac{4}{x}$

Mar 21, 2018

$\frac{4}{x}$

#### Explanation:

With algebraic fractions,a good place to start is to factorise if possible.

$\frac{4 x + 16}{x} \div \left(x + 4\right)$

$= \frac{4 \left(x + 4\right)}{x} \times \frac{1}{\left(x + 4\right)} \text{ } \leftarrow$ multiply and invert

Now you can cancel the factors - there is a multiplication sign between them.

$= \frac{4 \cancel{\left(x + 4\right)}}{x} \times \frac{1}{\cancel{\left(x + 4\right)}}$

$= \frac{4}{x}$