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Chapter 0: Problem 36

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

Short Answer

Expert verified
\(\frac{x+2}{x+3}\)

Step by step solution

01

Add Fractions

Since the denominators of both fractions are the same, the fractions can be added together. To add the fractions, combine the numerators over the common denominator: \( \frac{x^{2}-4 x + 4 x -4}{x^{2}-x-6} \)
02

Simplify the Numerator

Simplify the numerator by combining like terms: \( \frac{x^{2}-4}{x^{2}-x-6}\)
03

Factor the Numerator and Denominator

Factor the numerator as a difference of squares and the denominator as a quadratic: \( \frac{(x-2)(x+2)}{(x-2)(x+3)} \)
04

Simplify the Fraction

Remove common factors from the numerator and the denominator: \( \frac{x+2}{x+3}\)

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Most popular questions from this chapter

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

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