Algebra

[Shawn N]

Hello gents. Trying to help my girlfriend's daughter with some math & I didn't realize how bad I am with algebra. I'm not looking for an answer. Just an explanation on how this is solved. Any help is appreciated.

The question is:

Solve for the indicated variable

4/xy + 16/xz + 20/yz = 12

Solve for y.

I'm thinking divide by Y. I've been out of high school too long.

[zaza]

Multiply through by xyz and then collect terms....

[NickThissen]

What you want eventually is to get an expression that looks like
y = ...
(This is what solving for y means)

How do you do that? Well, in this case, y appears in a fraction as the denominator a few times. You don't want that, so how do you get rid of that? The answer is: multiply by y! Since
(1/y) * y = y/y = 1
you got rid of the y.

If there is some other stuff in the equation it works the same way:
(abc/y) * y = abc * (y/y) = abc
or
(abc/xy) * y = abc * (y/xy) = (abc/x) * (y/y) = abc/x

Visualize this too instead of just thinking of it as multiplication. If an y appears in the denominator, you multiply by y (to make "1") to get rid of it.

Of course, to keep the equation valid you'll have to multiply all other terms by y too. In this case that means:
4/xy + 16/xz + 20/yz = 12
4/x + 16y/xz + 20/z = 12y

Now the final step is to collect the terms that have y in them on one side, and put the remaining terms on the other side.