Question

How do you write the quotient in the simplest form?
x²-9/ 4x^2 divided by (x-3)

Answer 1

`\cfrac{x^2-9}{4x^2}/ (x-3)\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-3^2}}{4x^2}/ (x-3) \\\\\\ \cfrac{(x-3)(x+3)}{4x^2}/ (x-3)\implies \cfrac{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+3)}{4x^2}\cdot \cfrac{1}{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x+3}{4x^2}`

Answer 2

A. (x +3)/(4x²)

Explanation:

You want the simplified form of the quotient ((x²-9)/(4x²) ÷ (x -3).

Cancel common factors

The simplified form is found by cancelling common factors from the quotient's numerator and denominator.

`(x^2-9)/(4x^2)/(x-3)=(x^2-9)/(4x^2)*(1)/(x-3)=((x+3)(x-3))/(4x^2(x-3))=\boxed{(x+3)/(4x^2)}`