Question

Which expression is equivalent to the following complex fraction?

Answer 1

The correct answer is last option

Explanation:

It is given that,

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

To simplify (1/x - 1/y)

1/x - 1/y = (y - x)/xy

To simplify (1/x - 1/y)

1/x + 1/y = (y + x)/xy

To find equivalent expression

(1/x - 1/y)/(1/x +1/y = [(y - x)/xy]/[(y + x)/xy]

= (y - x)*xy/(y +x)*xy = (y - x)/(y + x)

Therefore the correct answer is last option

Answer 2

Answer: last option.

Explanation:

- Subtract the fractions that are in the numerator.

- Add the fractions that are in the denominator.

Then:

`((1)/(x)-(1)/(y))/((1)/(x)+(1)/(y))=((y-x)/(xy))/((y+x)/(xy))`

- Multiply the numerator of the fraction on the top by the denomianator of the fraction on the bottom.

- Simplify.

Then:

`=((y-x)(xy))/((y+x)(xy))=((y-x))/((y+x))`