# How do you simplify (2x) /( x + 4) div (6)/(x-1)?

May 15, 2016

$\frac{x \left(x - 1\right)}{3 \left(x + 4\right)}$

#### Explanation:

When we have a fraction divided by another fraction. Then leave the first fraction and multiply by the 'reciprocal' (flip the fraction over) of the second fraction.

In general: color(red)(|bar(ul(color(white)(a/a)color(black)(a/b÷c/d=a/bxxd/c)color(white)(a/a)|))

rArr(2x)/(x+4)÷6/(x-1)=(2x)/(x+4)xx(x-1)/6

Now that we have multiplication we can cancel any factors on the numerators with any common factors on the denominators.

$\Rightarrow \frac{{\cancel{2}}^{1} x}{x + 4} \times \frac{x - 1}{\cancel{6}} ^ 3 = \frac{x}{x + 4} \times \frac{x - 1}{3}$

We can now rewrite the product of these fractions as a single fraction.

In general : $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

rArrx/(x+4)xx(x-1)/3=(x(x-1))/(3(x+4)