Question

Find a common denominator, and subtract the following rational

expressions.
Simplify the final result, if possible.
6/x+1−x/x²−1

Answer 1

To subtract rational expressions, find a common denominator and rewrite the numerators. Then, simplify the expression if possible.

Step-by-step explanation:

To subtract rational expressions, we need to find a common denominator. In this case, the two denominators are x+1 and x²-1. To find a common denominator, we can factor the second denominator as (x+1)(x-1). So the common denominator is (x+1)(x-1).

To subtract the rational expressions, we need to rewrite the numerators with the common denominator. The first rational expression has a denominator of x+1, so we multiply the numerator and denominator of the second rational expression by x-1. This gives us:

6/(x+1) - x(x-1)/(x+1)(x-1)

Simplifying the expression, we get:

(6 - x(x-1))/(x+1)(x-1)

If further simplification is possible, you can expand the numerator and combine like terms.