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

Question

Julia Adams · Accepted Answer

#(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!

Kennedy Adams · Answer

undefined To simplify the expression (x+1)/(3y) + (x-2)/(4y) - (x+3)/(6y), you need to find a common denominator for the fractions. The common denominator in this case is 12y.

Multiplying the first fraction by 4/4, the second fraction by 3/3, and the third fraction by 2/2, we get:

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

Simplifying further, we have:

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

Combining the numerators, we get:

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

Simplifying the numerator, we have:

(5x + 4)/(12y)

Therefore, the simplified expression is (5x + 4)/(12y).