Rational Expressions Test – Algebra 2 Math (Printable PDF)

Question 1 Simplify with restrictions (2 points)

Simplify x² − 4x − 21x² − 49 and state the excluded values.

Question 2 Divide and simplify (3 points)

Divide: x² − 6x + 8x² + x ÷ x − 2x + 1.

Question 3 Subtract rational expressions (3 points)

Subtract and simplify: 5x + 4 − 3x − 6.

Question 4 Solve a rational equation (3 points)

Solve 2x + 5x + 6 = 1. Check each solution.

Question 5 Extraneous solution (2 points)

Solve xx − 6 = 3 + 6x − 6. Explain the result.

Question 6 Working together (3 points)

A community garden has weeds to clear. Rosa alone needs 12 hours and Theo alone needs 20 hours. How long will they need together?

Question 7 Solutions from a graph (2 points)

The graphs of y = 8x and y = x + 2 are shown.

1. Use the graph to state the solutions of 8x = x + 2. (1 point)
2. Verify one solution by substituting it. (1 point)

Question 8 Writing from excluded values (2 points)

The number line shows the excluded values of a rational expression whose numerator is 1. Write a possible expression with those excluded values.