Can we invert when there are more than two fractions?

[mwilliams82]

On a test question that I missed I found the following explanation... It follows:

The given equation...
1/y = 1/2a + 1/2b

The next step that they suggest is to find the common denominator and combine fractions as seen here:
1/y = (b + a)/2ab

And then they finally suggest inverting both sides:
y = 2ab/(a + b)

Though if we back it up to this point: 1/y = 1/2a + 1/2b... can we not just invert it to get y = 2a + 2b? Would this work? I tried this method and eventual got the wrong answer but I thought I saw this type of inversion in other equality problems before.

If somebody can help, thanks in advance!

[keanuxie]

5=2+3, is 1/5=1/2+1/3?
Hope it helps.

[Ben Ku]

Perhaps you're confusing ideas of proportions. You can invert fractions across an equation if you're multiplying or dividing terms, but not if you are adding or subtracting terms.

Suppose we have
(1/x) = (1/a)(1/b)
We can invert the terms, or "cross multiply", so it becomes
ab = x.

However, because you have terms you're adding/subtracting, you NEED to find a common denominator:
(1/x) = (1/a) + (1/b)
(1/x) = (b/ab) + (a/ab)
(1/x) = (b + a)/ab

Hope that helps.