Question

if x is the reciprocal of y, then x+y/x-y is equal to

Answer 1

Given, x is  reciprocal of  y.

x = 1/y

To find:

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

Putting x = 1/y

$\frac{x+y}{x-y}=\frac{\frac{1}{y}+y}{\frac{1}{y}-y}\\\;\\=\frac{\frac{1+y^{2}}{y}}{\frac{1-y^{2}}{y}}\\\;=\frac{1+y^{2}}{1+y^{2}}$

Hence, option 3) is  correct

Answer 2

Step-by-step explanation:

Given, x is reciprocal of y.

x = 1/y

To find:

\frac{x+y}{x-y}

x−y

x+y

Putting x = 1/y

\begin{gathered}\frac{x+y}{x-y}=\frac{\frac{1}{y}+y}{\frac{1}{y}-y}\\\;\\=\frac{\frac{1+y^{2}}{y}}{\frac{1-y^{2}}{y}}\\\;=\frac{1+y^{2}}{1+y^{2}}\end{gathered}

x−y

x+y

=

y

1

−y

y

1

+y

=

y

1−y

2

y

1+y

2

=

1+y

2

1+y

2

Hence, option 3) is correct