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Match the following rational expressions to their rewritten forms.

Rational Expressions:
x^2+x+4/x-2
x^2-x+4/x-2
x^2-4x+10/x-2
x^2-5x+16/x-2

Rewritten Forms:
(x-2)+6/x-2
(x+3)+10/x-2
(x+1)+6/x-2
(x-3)+10/x-2

Match The Following Rational Expressions To Their Rewritten Forms Rational Expressions X2x4x2 X2x4x2 X24x10x2 X25x16x2 Rewritten Forms X26x2 X310x2 X16x2 X310x2 class=

Sagot :

isyllus

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

[tex]1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}[/tex]

And the rewritten forms:

[tex](x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}[/tex]

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

[tex](x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}[/tex]

So, correct option is 3.

[tex](x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}[/tex]

So, correct option is 1.

[tex](x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}[/tex]

So, correct option is 2.

[tex](x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}[/tex]

So, correct option is 4.

The answer is also attached in the answer area.

View image isyllus
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