Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
This test covers simplifying, combining, and solving with rational expressions, including graph reading and a work problem. Factor completely, state excluded values when asked, and check every solution of an equation. No calculator is needed. The test is worth 20 points.
Standards: A-APR.D.6, A-APR.D.7, A-REI.A.2 · Level: Grade 11 Algebra 2
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.
- Use the graph to state the solutions of 8x = x + 2. (1 point)
- 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.
