5/x+2=x/3

Question

5/x+2=x/3

anonymous · Answer

First, let me ask real quickly is this supposed to be
$$\frac{5}{x+2}$$
or
$$\frac{5}{x}+2$$

anonymous · Answer

The first one.

anonymous · Answer

Ah, well then in the future you should type that at 5/(x+2) so people know :)
So, the first thing we should do whenever an equation has x in the denominator is see if we can do something to get x out of the denominator. So look at the equation and see if you can tell me what we would do to get x out of the denominator.

anonymous · Answer

Multiply it??! I DON"T KNOW?

anonymous · Answer

Multiplying is always a good way to get something out of the denominator. Good idea. So what are we going to multiply both sides by?

anonymous · Answer

x?

anonymous · Answer

Because that would make the equation x(5/x+2)=3

anonymous · Answer

But that would give you negative 1 and that's not right.

anonymous · Answer

Actually that would make the equation$$\frac{5x}{x+2} = \frac{x^2}{3}$$
Multiplying by x didn't get rid of either denominator.

anonymous · Answer

But if you multiply the x by it's self since it's division, you get x, so that would cancel them out.

anonymous · Answer

I'm skipping this problem it's too hard.

anonymous · Answer

Nope. You only cancel out if you multiply and divide by the same thing.
On the right side you're dividing by 3 and multiplying by x. That doesn't cancel out.

anonymous · Answer

Don't be a baby. Stick with it.

anonymous · Answer

Excuse me?!

anonymous · Answer

Doing the hard problems makes you better at math =) Let's finish this.

anonymous · Answer

Don't get good at giving up.