How do you simplify # (x+1)/(3y) + (x-2)/(4y) - (x+3)/(6y) #?

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Answer 1 · 2018-07-09T16:39:38

#(5x-8)/(12y)#

Since #12y# is the LCD of the denominators, that's what we want the denominator to be.

To achieve this, we can multiply the first fraction by #4/4#, the second by #3/3#, and the last by #2/2#. We now have

#(4(x+1))/(12y)+(3(x-2))/(12y)-(2(x+3))/(12y)#

This expression is equal to

#(4(x+1)+3(x-2)-2(x+3))/(12y)#

Let's distribute in the numerator to get

#(4x+4+3x-6-2x-6)/(12y)#

In the numerator, we can combine like terms to get

#(5x-8)/(12y)#

Since the terms have no common factors, we are done!

Hope this helps!