How to simplify algebraic fraction? such as..:

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

2 Answers
Jim G.
Mar 26, 2016

#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 #

Brandon
Apr 8, 2018

#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#

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