Question

Simplify the expression. $$\frac{x}{x^{2}-9}-\frac{3 x+1}{x^{2}-9}$$

Short answer

The simplified form of the given expression is \(-\frac{2x+1}{x^{2}-9}\).

Step-by-step solution

Recognize common denominators

Two fractions can be combined or subtracted if they share the same denominator. Here, both fractions have \(x^{2}-9\) as the denominator.

Combine the fractions

Subtract the second fraction from the first to combine them into a single fraction. This gives us \((x - (3x+1)) / (x^{2}-9)\) which simplifies to \((-2x -1) / (x^{2}-9)\).

Simplify the expression

Ensure that the expression is in its simplest form. As there are no common factors between the numerator and the denominator, the expression \(-2x -1 / x^{2}-9\) is the final simplified form.