Question

Reduce the algebraic fraction x - yx^2 - 1 X x - 2x^2 - y^2:

A. 1/x + 1

B. 1/x - 1

C. 1/x - y

D. 1/x + y

Answer 1

C. 1/x - y By isolating common factors and rearranging terms appropriately, the fraction can be expressed in its reduced form, which in this case is 1/x - y.

Explanation

The reduced form of the algebraic fraction is 1/x - y. To obtain this, factor out the common terms from the numerator and denominator of the fraction
`x - yx^2 - 1 ÷ x - 2x^2 - y^2.`Simplify by rearranging the terms to get 1/x - y.

In the process of reducing algebraic fractions, the aim is to factor out common terms from the numerator and denominator. Initially, factor out the common term 'x' from the numerator, which leaves 1 - yx - 1/x. Similarly, factor 'x' from the denominator to get 1
`- 2x - y^2/x`. Then, rearrange the terms in the simplified expression to get 1/x - y as the final reduced form.

Understanding the elements present in both the numerator and denominator is crucial to perform the simplification accurately. By isolating common factors and rearranging terms appropriately, the fraction can be expressed in its reduced form, which in this case is 1/x - y.