# Math Help - Fractions and equations.

1. ## 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)
$

2. 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?

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

4. 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:

$x = \frac{-b \pm \sqrt{b-4ac}}{2a}$

5. [quote=topher0805;

6. $
-2x^2 + 3x = - 77
$

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

X = 7 X = -5,5