Rational Expressions and Equations: Algebra 2 Math Test – PDF Download

Question 1: Simplify and restrict (2 points)

Simplify \(\frac{x^{2}-x-12}{x^{2}-16}\) and state all excluded values of \(x\).

Question 2: Divide rational expressions (2 points)

Simplify \(\frac{x^{2}-25}{x^{2}+2x}: \frac{x+5}{x+2}\) and state the excluded values.

Question 3: Add and subtract (3 points)

Simplify each expression.

1. \(\frac{3}{x+2}+\frac{4}{x-1}\) (1 point)
2. \(\frac{x}{x^{2}-4}-\frac{2}{x-2}\) (2 points)

Question 4: Rewrite a rational expression (2 points)

Rewrite \(\frac{x^{2}+5x+1}{x+2}\) in the form \(q(x)+\frac{r}{x+2}\).

Question 5: Solve and check (3 points)

Consider the equation \(\frac{x^{2}}{x-4}=\frac{3x+4}{x-4}\).

1. Find all values of \(x\) that result from clearing the denominators. (2 points)
2. Identify any extraneous solution and explain why it is extraneous. (1 point)

Question 6: Equation and graph (2 points)

The graphs of \(y=\frac{12}{x}\) and \(y=x+1\) are shown.

1. Solve \(\frac{12}{x}=x+1\) algebraically. (1 point)
2. Write the coordinates of the two intersection points. (1 point)

Question 7: Washing the vans (3 points)

Diego can wash all the team vans in \(10\) hours. Liam can wash them in \(15\) hours.

1. Write an equation for the time \(t\) in hours needed if they work together. (1 point)
2. Solve the equation. (2 points)

Question 8: Road trip (3 points)

Aisha drives \(120\) miles on the highway at \(r\) mph and then \(60\) miles through town at \((r-20)\) mph. The total driving time is \(3.5\) hours.

1. Write an equation for the total time. (1 point)
2. Find the highway speed \(r\). (2 points)

⬇ Download the Algebra 2 Rational Expressions and Equations test (PDF, 95 KB)

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