Question

Reduce this algebraic fraction (x-y/x^2-1)(x-1/x^2-y^2)

Answer 1

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

Explanation:

The given algebraic fraction is;

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

We factor using difference of two squares.

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

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

Cancel out the common factors;

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

Simplify;

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

Answer 2

1/(x+1)(x+y) is the simplification of (x-y/x²-1)(x-1/x²-y²).

Explanation:

We have given the expression:

(x-y/x²-1)(x-1/x²-y²)

We know that:

a²-b² = (a-b)(a+b) we get,

(x-y/(x+1)(x-1)) × ((x-1)/(x-y)(x+y))

We cancel out the like terms we get,

(1/x+1)×(1/x+y)

Simplification is :

1/(x+1)(x+y) is the simplification of (x-y/x²-1)(x-1/x²-y²).