Question

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

match the rational expressions to their rewritten forms.

\\((x + 5) + \frac{-2}{x - 1}\\)

\\((x - 1) + \frac{6}{x - 1}\\)

\\((2x + 1) + \frac{-6}{x - 1}\\)

\\((2x - 1) + \frac{6}{x - 1}\\)

tiles:
\\(\frac{x^2 + 4x - 7}{x - 1}\\)
\\(\frac{2x^2 - 3x + 7}{x - 1}\\)
\\(\frac{2x^2 - x - 7}{x - 1}\\)
\\(\frac{x^2 - 2x + 7}{x - 1}\\)

Explanation:

Find common denominators for the first two expressions

$$
LATEXBLOCK0
$$

Find common denominators for the remaining expressions

$$
LATEXBLOCK1
$$

Answer:

Left Expression	Matched Right Tile
\((x - 1) + \frac{6}{x - 1}\)	\(\frac{x^2 - 2x + 7}{x - 1}\)
\((2x + 1) + \frac{-6}{x - 1}\)	\(\frac{2x^2 - x - 7}{x - 1}\)
\((2x - 1) + \frac{6}{x - 1}\)	\(\frac{2x^2 - 3x + 7}{x - 1}\)