# 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.

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}