College Algebra Quiz: Add And Subtract Rational Expressions

What this quiz covers

This quiz focuses on Add And Subtract Rational Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $A = 5, B = -1$ (correct answer)
2. $A = 3, B = 1$
3. $A = 1, B = 3$
4. $A = -1, B = 5$

Explanation: To find A and B, we need to combine the left side over a common denominator. $\frac{A}{x-2} + \frac{B}{x+1} = \frac{A(x+1) + B(x-2)}{(x-2)(x+1)} = \frac{Ax + A + Bx - 2B}{(x-2)(x+1)} = \frac{(A+B)x + (A-2B)}{(x-2)(x+1)}$. For this to equal $\frac{4x+7}{(x-2)(x+1)}$, we need the numerators to be equal: $(A+B)x + (A-2B) = 4x + 7$. Comparing coefficients: $A + B = 4$ (coefficient of x) and $A - 2B = 7$ (constant term). From the first equation: $A = 4 - B$. Substituting into the second: $(4-B) - 2B = 7$, so $4 - 3B = 7$, which gives $-3B = 3$, so $B = -1$. Then $A = 4 - (-1) = 5$. Check: $A + B = 5 + (-1) = 4$ ✓ and $A - 2B = 5 - 2(-1) = 5 + 2 = 7$ ✓.