# How to simplify algebraic fraction? such as..:

## $\frac{4 a + 8 b}{6 a + 12 b}$

Mar 26, 2016

$\frac{2}{3}$

#### Explanation:

Factor both numerator and denominator and 'cancel' any common factors.

$\frac{4 a + 8 b}{6 a + 12 b} = \frac{4 \left(a + 2 b\right)}{6 \left(a + 2 b\right)}$

(a + 2b) is a common factor rArr (4cancel((a+2b))) /(6cancel((a+2b))

$\Rightarrow \frac{4 a + 8 b}{6 a + 12 b} = \frac{4}{6} = \frac{2}{3}$

Apr 8, 2018

$\frac{2}{3}$

#### Explanation:

To simplify any algebraic fraction, we factorise the top and bottom terms to find anything common so that the terms cancel out:

Factorising:

$4 a + 8 b \to 4 \left(a + 2 b\right)$

$6 a + 12 b \to 6 \left(a + 2 b\right)$

Putting factorised form into algebraic fraction:

$\frac{4 a + 8 b}{6 a + 12 b} \to \frac{4 \left(a + 2 b\right)}{6 \left(a + 2 b\right)}$

Since there is $\left(a + 2 b\right)$ in both terms, they cancel out.

-> (4cancel((a+2b))) /(6cancel((a+2b))

$\to \frac{4}{6}$

$\to \frac{2}{3}$