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Evaluate. \frac{x^2 + 4x + 1}{x - 5}= x + 9 + \frac{46}{x - 5}

Question:

Evaluate.

{eq}\frac{x^2 + 4x + 1}{x - 5}= x + 9 + \frac{46}{x - 5} {/eq}

Evaluating Expressions:


Evaluating expressions means finding the value of the unknown variable. This is done by simplifying the expression by combining the like terms and then finding the value of the unknown variable.

Answer and Explanation:


The expression is evaluated as follows.

$$\begin{align} &\frac{x^2 + 4x + 1}{x - 5}= x + 9 + \frac{46}{x - 5}\\ &\frac{x^2 + 4x + 1}{x - 5}=\frac{x(x-5)+9(x-5)+46}{x-5}\\ &x^2 + 4x + 1=x^2-5x+9x-45+46\\ &x^2-x^2+4x+5x-9x+1+45-46=0\\ &x\varepsilon \mathbf{R} \end{align} $$


Thus, we see that the two sides of the equation are identical.


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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