Need Exponent Help in Math?

Question

How Do You Get The Answer? (x+y)^-1/ x^-1+y^-1 , I think the answer is supposed to be xy/x+y or something close to that.

Answer 1

You need to fully parenthesize the expression, otherwise we can't tell what goes with what.

Answer 2

Obviously it should be

(x+y)^(-1)/ (x^(-1)+y^(-1)), but that looks messier, I think it was obvious enough without the extra parentheses.

Multiply top and bottom by xy, remembering xyx^(-1) = y

and xyy^(-1) = x:

xy(x+y)^-1/ (y+x)

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

because (x + y)^(-1) = 1/(x+y)

Hence we get

xy / (x + y)²

PS If you wanted to check this, you could sub, say,

x = 5, y = -2, in which case my answer gives - 10/9

The original expression gives

3^(-1) / (1/5 - 1/2)

= 1 / [3(-3/10)]

= -10/9