# Equations - Can't solve it!

• January 21st 2009, 08:22 AM
Pingu
Equations - Can't solve it!
Here's the thing:

$
\frac{3}{x-3}-\frac{1}{2x-6}=\frac{5}{6}
$

For this to add up, I need the bottom(?) to be the same, but how can I do that?
• January 21st 2009, 10:24 AM
Moo
Hello,
Quote:

Originally Posted by Pingu
Here's the thing:

$
\frac{3}{x-3}-\frac{1}{2x-6}=\frac{5}{6}
$

For this to add up, I need the bottom(?) to be the same, but how can I do that?

Note that $2x-6=2(x-3)$

So $\frac{3}{x-3}-\frac{1}{2x-6}=\frac{3}{x-3}-\frac{1/2}{x-3}$
And this easily adds up :)

In general, it's not that simple, you have to multiply both fractions by a factor such that the denominator becomes the highest common factor between the denominators.
• January 22nd 2009, 02:11 AM
hkerbest
Maybe you should do it like this.

$
\frac{6*3}{6(x-3)}-\frac{3*1}{3*2(x-3)}=\frac{5(x-3)}{6(x-3)}
$
• January 22nd 2009, 02:22 AM
princess_21
Quote:

Originally Posted by Pingu
Here's the thing:

$
\frac{3}{x-3}-\frac{1}{2x-6}=\frac{5}{6}
$

For this to add up, I need the bottom(?) to be the same, but how can I do that?

you should factor $2x-6$ first to get the common factor

$\frac{2(x-3)}{x-3}$

so the common factor is $x-3$

$\frac{3}{x-3}-\frac{1}{2x-6}=\frac{5}{6}$

$\frac{3*2}{2(x-3)}-\frac{1}{2x-6}=\frac{5}{6}$

$\frac{6}{2x-6}-\frac{1}{2x-6}=\frac{5}{6}$

$\frac{5}{2x-6}=\frac{5}{6}$

$5(6)=5(2x-6)$

$30=10x-30$

$60=10x$

$x=6$

:)