Question

How to simplify algebraic fraction? such as..:

`(4a +8b)/(6a+12b)`

Answer 1

`2/3`

Explanation:

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

`(4a + 8b)/(6a+ 12b) = (4(a + 2b))/(6(a + 2b))`

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

`rArr (4a+8b)/(6a+12b) = 4/6 = 2/3`

Answer 2

`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:

`4a+8b -> 4(a+2b)`

`6a+12b -> 6(a+2b)`

Putting factorised form into algebraic fraction:

`(4a + 8b)/(6a+ 12b) -> (4(a + 2b))/(6(a + 2b))`

Since there is `(a+2b)` in both terms, they cancel out.

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

`-> 4/6`

`-> 2/3`