Question

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

Answer 1

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`

Answer 2

`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`