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Chapter 0: Problem 40

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

Short Answer

Expert verified
The solution to the exercise is \(\frac{x-3}{x+3}\)

Step by step solution

01

Identify the expressions

The expression includes two fractions which have the same denominator. Fractions are: \(\frac{x^{2}-4 x}{x^{2}-x-6}\) and \(\frac{x-6}{x^{2}-x-6}\).
02

Subtract the Numerators

When the denominators of the fractions are same, subtraction can be done by subtracting the numerators. Doing so gives: \(\frac{x^{2}-4 x-(x-6)}{x^{2}-x-6}\) which simplifies further to \(\frac{x^{2}-4 x-x+6}{x^{2}-x-6}\)
03

Simplify the Numerator

Combine like terms in the numerator. The result gives: \(\frac{x^{2}-5 x+6}{x^{2}-x-6}\)
04

Factorize the Numerator and Denominator

Factorizing the expressions in the Numerator and Denominator gives us: \(\frac{(x-2)(x-3)}{(x-2)(x+3)}\)
05

Cancel the common factors

Cancel the common factors from the numerator and the denominator. The common factor is \((x鈭�2)\) which provides the simplified result: \(\frac{x-3}{x+3}\)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When checking a radical equation's proposed solution, I can substitute into the original equation or any equation that is part of the solution process.

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