Algebra 2 Rational Expressions Quiz – Free PDF

Contents

This algebra 2 rational expressions quiz asks 10 multiple-choice questions on rational expressions and equations, and each answer comes with a short explanation.

Answer these 10 multiple-choice questions on excluded values, simplifying, operations, rational equations, extraneous solutions, and work problems. Each question has exactly one correct answer, and the explanation after it names the key step.

Algebra 2Common Core: A-APR.D.6 · A-APR.D.7 · A-REI.A.2

🎯 Rational Expressions and Equations – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

For which values of \(x\) is \(\frac{x+2}{x^{2}-25}\) undefined?

A \(x=-2\) only

B \(x=5\) only

C \(x=5\) and \(x=-5\)

D \(x=2\) and \(x=-2\)

Question 2

Simplify \(\frac{x^{2}-9}{x^{2}-6x+9}\).

A \(\frac{x-3}{x+3}\)

B \(\frac{x+3}{x-3}\)

C \(\frac{x+3}{3}\)

D \(\frac{1}{x-3}\)

Question 3

Multiply and simplify: \(\frac{x}{x+2}\cdot\frac{x+2}{x-5}\).

A \(\frac{x}{x+5}\)

B \(\frac{1}{x-5}\)

C \(\frac{x}{x+2}\)

D \(\frac{x}{x-5}\)

Question 4

What is the LCD of \(\frac{1}{x^{2}-4}\) and \(\frac{1}{x+2}\)?

A \(x+2\)

B \((x-2)(x+2)^{2}\)

C \((x-2)(x+2)\)

D \(x-2\)

Question 5

Solve \(\frac{4}{x+1}=\frac{2}{x}\).

A \(x=1\)

B \(x=-2\)

C \(x=2\)

D \(x=-1\)

Question 6

The graph is the line \(y=x+2\) with a hole at \((3,5)\). Which expression has this graph?

A line with a hole at \((3,5)\).

A \(\frac{x^{2}-9}{x-3}\)

B \(\frac{x^{2}-2x-3}{x-3}\)

C \(\frac{x^{2}-x-6}{x+2}\)

D \(\frac{x^{2}-x-6}{x-3}\)

Question 7

The graphs show both sides of \(\frac{x}{x-3}=\frac{3}{x-3}\). How many solutions does the equation have?

The graphs of \(y=\frac{x}{x-3}\) (blue) and \(y=\frac{3}{x-3}\) (orange).

A \(1\): \(x=3\)

B \(1\): \(x=0\)

C \(0\): \(x=3\) is extraneous

D \(2\): \(x=3\) and \(x=-3\)

Question 8

Pipe A fills a tank in \(3\) hours and pipe B fills it in \(6\) hours. How long do they take together?

Time for each pipe to fill the tank alone.

A \(4.5\) hours

B \(2\) hours

C \(9\) hours

D \(3\) hours

Question 9

Rewrite \(\frac{x+5}{x+2}\) as a constant plus a fraction.

A \(1+\frac{7}{x+2}\)

B \(1-\frac{3}{x+2}\)

C \(1+\frac{3}{x}\)

D \(1+\frac{3}{x+2}\)

Question 10

Add: \(\frac{1}{x}+\frac{1}{x+1}\).

A \(\frac{2x+1}{x(x+1)}\)

B \(\frac{2}{2x+1}\)

C \(\frac{2}{x(x+1)}\)

D \(\frac{1}{x(x+1)}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards A-APR.D.6, A-APR.D.7, and A-REI.A.2: rewrite, operate on, and solve with rational expressions.
Excluded values are the zeros of the denominator, and they remain even after canceling.
Dividing means multiplying by the reciprocal; adding needs a common denominator.
Always check solutions of a rational equation: an extraneous solution makes a denominator zero.
Work problems add rates: \(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\).