# How do you simplify (2x - 3)/(1-5x) *( 5x-1)/(2x+3)?

May 19, 2018

$\frac{- 2 x + 3}{2 x + 3}$

#### Explanation:

First you want to do is times the numerators and the denominators together.. You can do this by multiplying the denominators together.
$\frac{\left(2 x - 3\right) \left(5 x - 1\right)}{\left(1 - 5 x\right) \left(2 x + 3\right)}$
Then you can multiply both sides by $- 1$
$\frac{- \left(2 x - 3\right) \left(5 x - 1\right)}{- \left(1 - 5 x\right) \left(2 x + 3\right)}$
Simplify this:
$\frac{\left(- 2 x + 3\right) \left(5 x - 1\right)}{\left(5 x - 1\right) \left(2 x + 3\right)}$
Then simplify out the $5 x - 1$ to get
$\frac{- 2 x + 3}{2 x + 3}$

May 19, 2018

See a solution process below:

#### Explanation:

First, multiply the fraction on the left by a $\frac{- 1}{-} 1$ which is a form of $1$. This will not change the value of the fraction but it will allow us to simplify the expression:

$\left(\frac{- 1}{-} 1 \cdot \frac{2 x - 3}{1 - 5 x}\right) \cdot \frac{5 x - 1}{2 x + 3} \implies$

$\frac{- 1 \left(2 x - 3\right)}{- 1 \left(1 - 5 x\right)} \cdot \frac{5 x - 1}{2 x + 3} \implies$

$\frac{- 2 x + 3}{- 1 + 5 x} \cdot \frac{5 x - 1}{2 x + 3} \implies$

$\frac{3 - 2 x}{5 x - 1} \cdot \frac{5 x - 1}{2 x + 3}$

Now, cancel common terms in the numerator an denominator:

$\frac{3 - 2 x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5 x - 1}}}} \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5 x - 1}}}}{2 x + 3} \implies$

$\frac{3 - 2 x}{1} \cdot \frac{1}{2 x + 3} \implies$

$\frac{\left(3 - 2 x\right) \cdot 1}{1 \cdot \left(2 x + 3\right)} \implies$

$\frac{3 - 2 x}{2 x + 3}$