Question

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

Answer 1

Answer

(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

Answer:

$\frac{y+1}{y-1}$

Step-by-step explanation:

To solve a complex fraction like $\frac{(1+\frac{1}{y} )}{(1-\frac{1}{y} )}$, take LCM of both the terms separately first to get:

$1+\frac{1}{y}$ = $\frac{y+1}{y}$

and

$1-\frac{1}{y} = \frac{y-1}{y}$

Now combine and divide these terms to get:

$\frac{\frac{y+1}{y} }{\frac{y-1}{y} }$

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

$\frac{y+1}{y-1}$

Therefore, the expression $\frac{y+1}{y-1}$ is equivalent to the given complex fraction.