Solve rational equations, and check for fake solutions

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Luz solves 4/(x − 5) = 3/(x − 6) in a notebook. What is x?

   9
2. 2.

   Milo solves 5/(x − 4) = 2/(x + 5) in pencil. What is x?

   -11
3. 3.

   Noah solves 6/(x − 3) = 4/(x − 1) from a math book. What is x?

   -3
4. 4.

   Pia clears the fractions in x²/(x − 4) = 16/(x − 4) and gets x = 4 or x = -4. Which are the solutions of the equation?

   • x = -4 only
   • No solution
   • x = 4 and x = -4
   • x = 4 only
5. 5.

   Ren clears the fractions in x²/(x − 3) = (x + 6)/(x − 3) and gets x = 3 or x = -2. Which are the solutions of the equation?

   • No solution
   • x = -2 only
   • x = 3 and x = -2
   • x = 3 only
6. 6.

   Tala clears the fractions in x²/(x + 5) = (10 − 3x)/(x + 5) and gets x = -5 or x = 2. Which are the solutions of the equation?

   • x = -5 and x = 2
   • No solution
   • x = -5 only
   • x = 2 only
7. 7.

   Zee clears the fractions in x²/(x − 1) = (6 − 5x)/(x − 1) and gets x = 1 or x = -6. Which are the solutions of the equation?

   • x = 1 only
   • x = 1 and x = -6
   • No solution
   • x = -6 only
8. 8.

   Ari multiplies every term of x/(x + 2) + 3 = 4/(x + 2) by x + 2 on a worksheet. Which equation does that give?

   • x + 3 = 4
   • x + 3(x + 2) = 4
   • x + 3x + 2 = 4
   • x + 3 = 4(x + 2)
9. 9.

   Bo multiplies every term of x/(x − 5) + 2 = 7/(x − 5) by x − 5 in a notebook. Which equation does that give?

   • x + 2(x − 5) = 7
   • x + 2 = 7
   • x + 2 = 7(x − 5)
   • x + 2x − 5 = 7
10. 10.

    Esme multiplies every term of x/(x + 1) + 4 = 9/(x + 1) by x + 1 in pencil. Which equation does that give?

    • x + 4 = 9
    • x + 4x + 1 = 9
    • x + 4 = 9(x + 1)
    • x + 4(x + 1) = 9