How do you simplify # (5y+3)/(y+2) - (2y-3)/(y+2)#?

2 Answers
Mar 8, 2018

Combine the two fractions together since they both have the same denominator.

Explanation:

Let's use an easier example to illustrate this. #1/2+2/2=3/2#. This is done by combining the two fractions, which both have the same denominator (2 in this case). #1/2+2/2=(1+2)/2=3/2#

Let's use this to solve our problem:

#(5y+3)/(y+2)-(2y-3)/(y+2)#

#(5y+3-(2y-3))/(y+2)#

#(5y+3-2y+3)/(y+2)#

#(3y+6)/(y+2)#

While we may seem like we're done, we haven't completely simplified our fraction. Let's factor out a 3 in the numerator to get our answer:

#(3(y+2))/(y+2)#

#3(cancel(y+2))/cancel(y+2) = 3#

Mar 8, 2018

#3#

Explanation:

#(5y+3)/(y+2)-(2y-3)/(y+2)#

#:.=((5y+3)-(2y-3))/(y+2)#

#:.=(5y+3-2y+3)/(y+2)#

#:.=(3y+6)/(y+2)#

#:.=(3 cancel((y+2))^1)/cancel(y+2)^1#

#:.=3#