Algebra 2 Rational Expressions Quiz: 10 Questions with Explanations

A \(x = 7\)B \(x = -7\)C \(x = 0\)D \(x = 5\)

The denominator is 0 when x + 7 = 0, so x = -7.

A \(x – 2\)B \(x^{2} – 2\)C \(\frac{x}{2}\)D \(x + 2\)

Factor the numerator: (x – 2)(x + 2) and cancel x – 2.

A \((2, 4)\)B \((-2, 0)\)C \((2, 0)\)D \((0, 2)\)

The canceled factor x – 2 leaves a hole at x = 2, where y = x + 2 = 4.

A \(\frac{x}{x – 1}\)B \(\frac{x^{2}}{x + 5}\)C \(\frac{x}{x + 5}\)D \(x + 5\)

Cancel the common factor x – 1.

A \(\frac{2 + x}{2x}\)B \(\frac{2}{x + 2}\)C \(\frac{1}{x + 2}\)D \(\frac{x + 2}{x}\)

The LCD is 2x: 2/(2x) + x/(2x) = (2 + x)/(2x). Adding denominators is a common error.

A \(\frac{8}{x^{3}}\)B \(\frac{2}{x}\)C \(\frac{1}{2x}\)D \(\frac{x}{2}\)

Multiply by the reciprocal: 2/x · x²/4 = 2x²/(4x) = x/2.

A 5 hoursB 2.4 hoursC 10 hoursD 12 hours

Combined rate 5/12 per hour gives 12/5 = 2.4 hours.

A \(x = 3 only\)B \(x = -1\)C \(x = 3 and x = -3\)D \(x = 9\)

x² – 9 = (x – 3)(x + 3) = 0 gives x = 3 or x = -3.

A Canceling the 4s to get x + 1B Writing it as x/4 + 1C Stating that the denominator is never 0D Leaving it as it is

Only factors can be canceled. The 4 in the numerator is a term, not a factor.

A \(x – 5\)B \(x – 4\)C \(x + 4\)D \(x^{2} – 4\)

x² – 9x + 20 = (x – 4)(x – 5). Cancel x – 5 to get x – 4.