Problem 36 - College Algebra

Question

Add or subtract as indicated. $$\frac{x^{2}-4 x}{x^{2}-x-6}+\frac{4 x-4}{x^{2}-x-6}$$

Step-by-Step Solution

Answer

The simplified form of the given expression is \(\frac{{x^{2} - 4}}{{x^{2} - x - 6}}\).

Step 1: Combine the Similar Terms

As both fractions have the same denominator, they can be combined. This results in \(\frac{{x^{2} - 4x + 4x - 4}}{{x^{2} - x - 6}}\).

Step 2: Simplify the Numerator

Simplify the numerator by combining the similar terms. \(-4x + 4x = 0\), so the fraction becomes \(\frac{{x^{2} - 4}}{{x^{2} - x - 6}}\) after this simplification.

Step 3: No Simplification is Possible

Check if any further simplification is possible by trying to reduce the fraction. It's seen that no common terms exist in the numerator and the denominator, so no further simplification is possible and this is our final expression.