# algebra, solve x

• Feb 6th 2007, 12:16 AM
desmon
algebra, solve x
Hi,

heres the question i was working on, which originally asked to add some algebraic fractions. That part was fine but I'm asked to find x and am stuck here.

3x^2 + 5x - 2
------------- = 0
3x^2 + 2x

Any help is greatly appreciated.

Thanks
• Feb 6th 2007, 01:31 AM
AlvinCY
Quote:

Originally Posted by desmon
Find x.

$\displaystyle \frac{3x^2 + 5x - 2}{3x^2 + 2x} = 0$

Any help is greatly appreciated.

Thanks

$\displaystyle \frac{3x^2 + 5x - 2}{3x^2 + 2x} = 0$ inplies that $\displaystyle 3x^2 + 5x - 2 = 0$ and that $\displaystyle 3x^2 + 2x \not = 0$

Solving $\displaystyle 3x^2 + 5x - 2 = 0$

$\displaystyle 3x^2 + 5x - 2 = 0$
$\displaystyle 3x^2 + 6x - x - 2 = 0$
$\displaystyle 3x(x + 2) - (x + 2) = 0$
$\displaystyle (3x - 1)(x + 2) = 0$

So $\displaystyle x = \frac{1}{3}$ or $\displaystyle x = -2$

Checking the condition that $\displaystyle 3x^2 + 2x \not = 0$

$\displaystyle 3x^2 + 2x \not = 0$
$\displaystyle x(3x + 2) \not = 0$
$\displaystyle x \not = 0$ or $\displaystyle x \not = -\frac{2}{3}$