# Fractions just can't think of what to do here

• Mar 26th 2013, 07:48 AM
uperkurk
Fractions just can't think of what to do here
$\displaystyle \frac{x}{x+8}=\frac{2}{3}$

The answer is $\displaystyle x=16$ but I can't see how they're coming to this answer...
• Mar 26th 2013, 07:53 AM
Plato
Re: Fractions just can't think of what to do here
Quote:

Originally Posted by uperkurk
$\displaystyle \frac{x}{x+8}=\frac{2}{3}$

The answer is $\displaystyle x=16$ but I can't see how they're coming to this answer...

If $\displaystyle x\ne -8$ then $\displaystyle \frac{x}{x+8}=\frac{2}{3}$ is same as $\displaystyle 3x=2x+16$.
• Mar 26th 2013, 08:14 AM
uperkurk
Re: Fractions just can't think of what to do here
Quote:

Originally Posted by Plato
If $\displaystyle x\ne -8$ then .

How can I know that $\displaystyle x\ne -8$? Also can you show me how exactly you got from $\displaystyle \frac{x}{x+8}=\frac{2}{3}$ to $\displaystyle 3x=2x+16$
• Mar 26th 2013, 10:08 AM
HallsofIvy
Re: Fractions just can't think of what to do here
The reason for "$\displaystyle x\ne -8$" is that, in that case, the fraction on the left is not defined.

And you go from one equation to the other by multiplying both sides by 3(x+ 8), the product of the two denominators.