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Kruka [31]
4 years ago
15

Simplify the following rational expressions:

Mathematics
2 answers:
DiKsa [7]4 years ago
8 0

\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}

Y_Kistochka [10]4 years ago
7 0

Answer:

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.

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