Simplify: \frac{x^{2} - 3x - 18}{x + 3} A. x - 3 B. x - 6; x not equal to -3 C. x - 6; x not...


Simplify: {eq}\quad\displaystyle\frac{x^{2} - 3x - 18}{x + 3} {/eq}

A. {eq}\;\displaystyle x - 3 {/eq}

B. {eq}\displaystyle\;x - 6; \quad x \neq -3 {/eq}

C. {eq}\displaystyle\;x - 6; \quad x \neq 6 {/eq}

D. {eq}\displaystyle\;\frac{1}{x + 3}; \quad x \neq -3 {/eq}

Simplifying Expressions:

When we have to simplify polynomial fractions that are in their expanded form, we have to factorize the denominator and the numerator both (if possible). This is so that we can remove the common factors of the denominator and numerator and have a simplified expression.

Answer and Explanation:

The expression is simplified as follows.

$$\begin{align} &\frac{x^{2} - 3x - 18}{x + 3}\\ =&\frac{x^{2} -6x+ 3x - 18}{x + 3}\\ =&\frac{x(x-6)+3(x-6)}{x + 3}\\ =&\frac{(x+3)(x-6)}{(x+3)}\\ =&x-6 \end{align} $$

{eq}x\neq-3 {/eq} because if the variable takes this value then, in the denominator of the original expression, we get a value of 0. The fraction then becomes undefined. So, the correct option is B.

Learn more about this topic:

Practice Simplifying Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 7

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