Question

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

Answer 1

Answer:

$\frac{r^2-10}{(r+4)(r+1)}$

Step-by-step explanation:

We want to evaluate:

$\frac{r+2}{r+4}-\frac{3}{r+1}$

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

$\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}$

Expand the numerator:

$\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}$

$\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}$

$\frac{r^2-10}{(r+4)(r+1)}$

Answer 2

Answer:

$\frac{ r^2-10}{(r+4)(r+1)}$

Step-by-step explanation:

$\frac{r+2}{r+4} - \frac{3}{r+1}$

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

$\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}$

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

3(r+4) becomes 3r+12

$\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}$

$\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}$

combine like terms

$\frac{ r^2-10}{(r+4)(r+1)}$