# Solution to Simplification of Algebraic Expression

• October 1st 2010, 02:21 PM
BIOS
Solution to Simplification of Algebraic Expression
The following expression i am looking to confirm whether my answer is correct:

$\displaystyle \frac {6a+3}{2a^2+5a+2}$

For the above expression my answer is $\displaystyle \frac {3}{a+2}$

The book however has the answer as $\displaystyle \frac {3}{2a+1}$

Can anyone verify if i'm incorrect in my answer and why?

Cheers

BIOS
• October 1st 2010, 02:37 PM
skeeter
Quote:

Originally Posted by BIOS
The following expression i am looking to confirm whether my answer is correct:

$\displaystyle \frac {6a+3}{2a^2+5a+2}$

For the above expression my answer is $\displaystyle \frac {3}{a+2}$

The book however has the answer as $\displaystyle \frac {3}{2a+1}$

Can anyone verify if i'm incorrect in my answer and why?

Cheers

BIOS

$\displaystyle \frac {6a+3}{2a^2+5a+2} = \frac{3(2a+1)}{(2a+1)(a+2)} = \frac{3}{a+2} \, ; \, a \ne -\frac{1}{2}$
• October 1st 2010, 02:57 PM
1005
it's always good to have methods to check if your answers are right (because it in the real world you don't have a solution to check it against)

for example, here you could have evaluated the 3 expressions with a simple a such as 2:
$\frac{12+3}{8+10+2}=\frac{15}{20}=\frac{3}{4}$
$\frac{3}{2+2}=\frac{3}{4}$
$\frac{3}{4+1}=\frac{3}{5}\ne\frac{3}{4}$
so you could have now comfortably rejected the book's answer without verification from an authority figure.