# simplifying two fractions

• May 10th 2006, 04:05 AM
simplifying two fractions
Hi sorry about the over flow of questions today just going over some stuff for and exam tomorrow.

how would you simplify the following fraction into a single fraction?

$\displaystyle \frac{x}{x^2+4x+3}-\frac{2}{x^2+3x+2}$

cheers
• May 10th 2006, 07:43 AM
earboth
Quote:

Hi sorry about the over flow of questions today just going over some stuff for and exam tomorrow.

how would you simplify the following fraction into a single fraction?

$\displaystyle \frac{x}{x^2+4x+3}-\frac{2}{x^2+3x+2}$
cheers

Hello,

1. Factorize the denominators. You'll get:
$\displaystyle x^2+4x+3 = (x+1)(x+3)$
$\displaystyle x^2+3x+2 = (x+1)(x+2)$

2. Thus the lcd = (x+1)(x+2)(x+3).

3. Transform the fractions and you'll get:

$\displaystyle \frac{x(x+2)}{(x+1)(x+2)(x+3)}-\frac{2(x+3)}{(x+1)(x+2)(x+3)}$

$\displaystyle \frac{x^2+2x-2x-6}{(x+1)(x+2)(x+3)}$ = $\displaystyle \frac{x^2-6}{(x+1)(x+2)(x+3)}$

Greetings

EB
• May 10th 2006, 09:01 AM