Question

Which expression is equivalent to the following complex fraction? 1+1/y /1-1/y

Answer 1

(y + 1) / (y - 1)

Explanation

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

1+1/y = 1/y(y + 1)

= (1/y)(y + 1)

1 - 1/y = (1/y)(y - 1)

= (1/y)(y - 1)

∴ (1/y)(y + 1) / (1/y)(y - 1) = (y + 1) / (y - 1)

Answer 2

`(y+1)/(y-1)`

Explanation:

To solve a complex fraction like
`((1+(1)/(y) ))/((1-(1)/(y) ))`, take LCM of both the terms separately first to get:

`1+(1)/(y)` =
`(y+1)/(y)`

and

`1-(1)/(y) = (y-1)/(y)`

Now combine and divide these terms to get:

`((y+1)/(y) )/((y-1)/(y) )`

The term
`y` in both the denominators will be cancelled out by each other and you will be left with:

`(y+1)/(y-1)`

Therefore, the expression
`(y+1)/(y-1)` is equivalent to the given complex fraction.