# Fractions and equations.

• Feb 3rd 2009, 09:58 AM
Pingu
Fractions and equations.
Im having a little trouble with this one:

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

I can't find a decent "bottom half" fraction for this. Im thinking

$
5(x-2)(x+3)
$
• Feb 3rd 2009, 10:17 AM
Bruce
Quote:

Originally Posted by Pingu
Im having a little trouble with this one:

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

I can't find a decent "bottom half" fraction for this. Im thinking

$
5(x-2)(x+3)
$

Your denominator is good. Now set that as your denominator for each fraction. You will then have to multiply the top by the same thing you multiplied the bottom by. So:

$\frac {3 * 5(x+3)}{5(x - 2)(x + 3)} - \frac {2 * 5(x -2)}{5(x-2)(x+3)} = \frac {2 * (x-2)(x+3)}{5(x-2)(x+3)}$

then you simplify:

$\frac {15x + 45}{5(x-2)(x+3)} - \frac {10x - 20}{5(x-2)(x+3)} = \frac {2x^2 + 2x - 12}{5(x-2)(x+3)}$

Do the subtracting...

$\frac {5x + 65}{5(x-2)(x+3)} = \frac {2x^2 + 2x - 12}{5(x-2)(x+3)}$

Multiply both sides by the same denominator...

$5x + 65 = 2x^2 + 2x - 12$

Can you do it from here?
• Feb 3rd 2009, 10:20 AM
Pingu
Yes, I've tried that, and it turns out pretty messy. The correct number for X is 7, If my calculator is correct.
• Feb 3rd 2009, 10:22 AM
topher0805
Quote:

Originally Posted by Pingu
Yes, I've tried that, and it turns out pretty messy. The correct number for X is 7, If my calculator is correct.

It shouldn't be messy. You just need to get it into quadratic form and use this formula:

$x = \frac{-b \pm \sqrt{b-4ac}}{2a}$
• Feb 3rd 2009, 10:24 AM
Pingu
[quote=topher0805;
• Feb 3rd 2009, 10:31 AM
hkerbest
$
-2x^2 + 3x = - 77
$

$
(-2x+3)(x-0) = - 77
$

X = 7 X = -5,5