Question

What is the difference in simplest form? n^2+3n+2/n^2+5n+6 - 2n/n+3

Answer 1

\(\displaystyle \bf \frac{n^2+3n+2}{n^2+5n+6}-\frac{2n}{n+3}\)

This look correct Ashley?

Answer 2

Yes thats correct @austinL

Answer 3

Since you are subtracting fractions you need a common denominator.
Start by factoring the numerator and denominator of the left fraction.

Answer 4

Here's a start, the numerator of the left piece factors into (n+2)(n+1)

Answer 5

Right. and the denominator is (n+2)(n+3)

Answer 6

The n+2's cancel and you just subtract across

Answer 7

so is it 1/n+3?

Answer 8

\[\frac{ (n+2)(n+1) }{ (n+3)(n+2) } = \frac{ (n+1) }{ (n+3) } \]
\[\large \frac{ n+1 }{ n+3 }-\large \frac{ 2n }{ n+3 } = \frac{ n+1-2n }{ n+3 } = \frac{ n+1-2n }{ n+3 } =\frac{ 1-n }{ n+3 } \]

Answer 9

oops, there's a double in there

Answer 10

Okay. I get it. Thanks @bibby and @mathstudent55.