Question

Which expression is equivalent to the following complex fraction?

Answer 1

Answer: last option.

Step-by-step explanation:

- Subtract the fractions that are in the numerator.

- Add the  fractions that are in the denominator.

Then:

$\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}=\frac{\frac{y-x}{xy}}{\frac{y+x}{xy}}$

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

- Simplify.

Then:

$=\frac{(y-x)(xy)}{(y+x)(xy)}=\frac{(y-x)}{(y+x)}$

Answer 2

Answer:

The correct answer is last option

Step-by-step 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