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

Step by step solution

01

Combine the Similar Terms

As both fractions have the same denominator, they can be combined. This results in \(\frac{{x^{2} - 4x + 4x - 4}}{{x^{2} - x - 6}}\).
02

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.
03

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.

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Most popular questions from this chapter

Simplify by reducing the index of the radical. $$\sqrt[6]{x^{4}}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

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