How do you simplify #3/(x+2) + 6/(x-1)#?

1 Answer
mimi
Oct 9, 2015

By finding the Lowest Common Multiple (LCM)

Ans: #(9x+9)/((x+2)(x-1))#

Explanation:

#3/(x+2)+6/(x-1)#

Compare the denominators of #3# and #6#.

Notice that the denominator of #3# lacks #x-1#, while the denominator of #6# lacks #x+2#.

Therefore, multiply #3# by #x-1#, and multiply #6# by #x+2#. Their sum will make up the numerator of your final expression.

To obtain the denominator of your final expression, multiply #x+2# by #x-1#.

#(3(x-1)+6(x+2))/((x+2)*(x-1))#

#(3x-3+6x+12)/((x+2)(x-1))#

#(9x+9)/((x+2)(x-1))#

The numerator and the denominator don't contain any common numbers that could be canceled out, so the expression can't be further simplified and this will be your final answer

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