Math Question?

Question

Divide ((X+Y)\X) by the sum (1/x) and (1/y)

I got the answer to be Y, is that correct?

Answer 1

So you want to solve

[(x + y)/x] / [1/x + 1/y]

To simplify this, note that it's a complex fraction. To simplify ANY complex fraction, multiply top and bottom by the LCD (lowest common denominator). In this case, it's xy. Multiplying top and bottom by xy should get rid of all fractions, but you need to keep track of what gets left behind. Below is what gets left behind:

y(x + y) / [y + x]

Addition is commutative; y + x = x + y.

y(x + y) / [x + y]

Now, we can cancel (x + y) on the top and bottom, leaving us with only:

y

Answer 2

No, I got (Xsquared + 2XY + Ysquared)/X

But it seems I made an error. Note that you can always check your result by plugging in simple numbers like 2 and 3 for X and Y.

Answer 3

[(x + y)/x]/(1/x + 1/y)
= [(x + y)/x]/[(x + y)/xy]
Multiply the numerator by y/y
[y(x+y)/xy]/[(x + y)/xy]
Cancel out 'x + y' and 'xy'
You are left with y
Your answer is correct