# How do you reduce \frac { 30x - 10} { 70x + 90}?

Mar 3, 2018

Factoring out common factors, we can reduce any given expression provided that there are common factors.

#### Explanation:

A look at our expression shows us that all the terms are some multiples of $10$. Which means that we can factor 10 from numerator and denominator and cancel them out.

• $30 x - 10$ can be written as $10 \left(3 x - 1\right)$
• $70 x + 10$ can be written as $10 \left(7 x + 1\right)$

Now, divide them

$\frac{10 \left(3 x - 1\right)}{10 \left(7 x + 1\right)} = \frac{3 x - 1}{7 x + 1}$

$\frac{3}{7} \left(\frac{x - \frac{1}{3}}{x + \frac{9}{7}}\right)$

#### Explanation:

$\frac{30 x - 10}{70 x + 90}$
=(30(x-1/3))/(70(x+9/7)
$= \frac{3}{7} \left(\frac{x - \frac{1}{3}}{x + \frac{9}{7}}\right)$