Question

drag the tiles to the correct boxes to complete the pairs.

match the rational expressions to their rewritten forms.

rewritten form
\\((x - 2) + \frac{6}{x - 2}\\)
\\((x + 3) + \frac{10}{x - 2}\\)
\\((x + 1) + \frac{6}{x - 2}\\)
\\((x - 3) + \frac{10}{x - 2}\\)

expression

tiles:
\\(\frac{x^2 + x + 4}{x - 2}\\)
\\(\frac{x^2 - 4}{x - 2}\\)
\\(\frac{x^2 + 4x + 10}{x - 2}\\)
\\(\frac{x^2 - 5x + 16}{x - 2}\\)

Explanation:

Simplify the first rewritten form

$$ (x - 2) + \frac{6}{x - 2} = \frac{(x - 2)^2 + 6}{x - 2} = \frac{x^2 - 4x + 4 + 6}{x - 2} = \frac{x^2 - 4x + 10}{x - 2} $$

Simplify the second rewritten form

$$ (x + 3) + \frac{10}{x - 2} = \frac{(x + 3)(x - 2) + 10}{x - 2} = \frac{x^2 + x - 6 + 10}{x - 2} = \frac{x^2 + x + 4}{x - 2} $$

Simplify the third and fourth rewritten forms

$$ (x + 1) + \frac{6}{x - 2} = \frac{(x + 1)(x - 2) + 6}{x - 2} = \frac{x^2 - x - 2 + 6}{x - 2} = \frac{x^2 - x + 4}{x - 2} $$

$$ (x - 3) + \frac{10}{x - 2} = \frac{(x - 3)(x - 2) + 10}{x - 2} = \frac{x^2 - 5x + 6 + 10}{x - 2} = \frac{x^2 - 5x + 16}{x - 2} $$

Answer:

Match the rational expressions to their rewritten forms:

• \((x - 2) + \frac{6}{x - 2}\) \(

ightarrow\) <blank>\(\frac{x^2 - 4x + 10}{x - 2}\)</blank>

• \((x + 3) + \frac{10}{x - 2}\) \(

ightarrow\) <blank>\(\frac{x^2 + x + 4}{x - 2}\)</blank>

• \((x + 1) + \frac{6}{x - 2}\) \(

ightarrow\) <blank>\(\frac{x^2 - x + 4}{x - 2}\)</blank>

• \((x - 3) + \frac{10}{x - 2}\) \(

ightarrow\) <blank>\(\frac{x^2 - 5x + 16}{x - 2}\)</blank>