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Simplify the following expression: \frac {x^2(x+2)-x-(x-2)^2+7}{x^2+3}

Question:

Simplify the following expression: {eq}\frac {x^2(x+2)-x-(x-2)^2+7}{x^2+3} {/eq}

Algebraic Expression:

The objective of the given problem is to simplify the expression in numerator and denominator. To simplify the given function, we first expand the expression in the numerator and simplify the numerator. After that, cancel out the common factors of both numerator and denominator to get the simplified form.

Answer and Explanation:

We are given that {eq}\displaystyle \frac {x^2(x+2)-x-(x-2)^2+7}{x^2+3} {/eq}

Using the Algebraic identities

{eq}\displaystyle (x +y)^2 = x^2 + y^2 + 2xy {/eq}

Thus,

{eq}\begin{align*} \displaystyle \frac {x^2(x+2)-x-(x-2)^2+7}{x^2+3} & = \displaystyle \frac {x^3 + 2x^2 -x-(x^2 +4 -4x) +7}{x^2+3}\\ & = \displaystyle \frac {x^3 + 2x^2 -x- x^2 - 4 +4x +7}{x^2+3}\\ & = \displaystyle \frac {x^3 + x^2 +3x +3}{x^2+3}\\ & = \displaystyle \frac {x^2(x+1) +3(x +1)}{x^2+3}\\ & = \displaystyle \frac {(x^2 +3)(x +1)}{x^2+3}\\ & = \displaystyle (x +1) \end{align*} {/eq}


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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