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

How do you write the quotient in the simplest form? x²-9/ 4x^2 divided by (x-3)-example-1

2 Answers

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\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}

User Jcgrowley
by
4.7k points
3 votes

Answer:

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)}

User PJL
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