Question

What is the difference r+2/r+4-3/r+1

Answer 1

`(r^2-10)/((r+4)(r+1))`

Explanation:

We want to evaluate:

`(r+2)/(r+4)-(3)/(r+1)`

We collect the least common multiple of the denominators to get:

`((r+2)(r+1)-3(r+4))/((r+4)(r+1))`

Expand the numerator:

`(r^2+3r+2-3r-12)/((r+4)(r+1))`

`(r^2-3r+3r+2-12)/((r+4)(r+1))`

`(r^2-10)/((r+4)(r+1))`

Answer 2

`( r^2-10)/((r+4)(r+1))`

Explanation:

`(r+2)/(r+4) - (3)/(r+1)`

To simplify the fractions we take common denominator

LCD is (r+4)(r+1)

we try to get same denominator on both fraction

multiply the first fraction by r+1 and second fraction by r+4

`((r+2)(r+1))/((r+4)(r+1)) - (3(r+4))/((r+1)(r+4))`

(r+2)(r+1) becomes r^2 +3r+2

3(r+4) becomes 3r+12

`( r^2 +3r+2)/((r+4)(r+1)) - (3r+12))/((r+1)(r+4))`

`( r^2 +3r+2-3r-12)/((r+4)(r+1))`

combine like terms

`( r^2-10)/((r+4)(r+1))`