Question

Perform the indicated operation and simplify the result.

Answer 1

`(x-y)/(x^(2) -1)`*
`(x-1)/(x^(2)-y^(2))`=

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

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

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

Answer 2

The answer is 1/(x+1)(x+y)

Explanation:

Given the equation

x-y/x²-1 × x-1/x²-y²

We will apply the difference of two square to solve the equation. According to the rule, if a and b are real numbers;

a²-b² = (a+b)(a-b)

Therefore x²-1 = x²-1² = (x+1)(x-1)

Similarly, x²-y² = (x+y)(x-y)

Substituting this functions in the question we have;

x-y/x²-1 × x-1/x²-y²

= x-y/(x+1)(x-1) × x-1/(x+y)(x-y)

x-y will cancel x-y and x-1 will also cancel out x-1 to reduce the equation to;

x-y/x²-1 × x-1/x²-y² = 1/x+1 × 1/x+y

= 1/(x+1)(x+y) which is the simplified form of the equation