Question

Simplify the following rational expressions:

x^2 - 16 | x^3 + 27

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x^3 - 4x^2 | x^2 - 9

Answer 1

`\bf \cfrac{x^2-16}{x^3-4x^2}\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-4^2}}{x^2(x-4)}\implies \cfrac{~~\begin{matrix} (x-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+4)}{x^2~~\begin{matrix} (x-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x+4}{x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^3+27}{x^2-9}\implies \cfrac{\stackrel{\textit{sum of cubics}}{x^3+3^3}}{\underset{\textit{difference of squares}}{x^2-3^2}}`

`\bf \cfrac{~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x^2-3x+3^2)}{(x-3)~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x^2-3x+9}{x-3}`

Answer 2

1. x^2−16

2. x^3+27

3. x^3−4x^2

4. x^2−9

Explanation: Step-by-step

1. Let's simplify step-by-step.

x2−16

There are no like terms.

2. Let's simplify step-by-step.

x3+27

There are no like terms.

3. Let's simplify step-by-step.

x3−4x2

There are no like terms.

4.Let's simplify step-by-step.

x2−9

There are no like terms.