Solve rational equations, and check for fake solutions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Luz solves 5/(x − 2) − 2/(x + 3) = 4/(x² + x − 6) in a notebook. What is x?

   -5
2. 2.

   Milo solves 3/(x − 3) + 1/(x − 1) = 18/(x² − 4x + 3) in pencil. What is x?

   6
3. 3.

   Noah solves 4/(x − 4) − 3/(x + 2) = 6/(x² − 2x − 8) from a math book. What is x?

   -14
4. 4.

   Ren solves x/(x − 3) = 3/(x − 3) + 2 in a notebook. Which describes the solutions?

   • x = -3
   • No solution
   • x = 3
   • Every number
5. 5.

   Tala solves x²/(x + 5) = 25/(x + 5) in pencil. Which describes the solutions?

   • x = -5 and x = 5
   • x = 5
   • x = -5
   • No solution
6. 6.

   Zee solves (x² − 2x)/(x − 4) = 8/(x − 4) from a math book. Which describes the solutions?

   • No solution
   • x = -2 and x = 4
   • x = 4
   • x = -2
7. 7.

   Two hoses fill Bo's garden barrel together in 6 minutes. The big hose alone takes 10 minutes. How many minutes does the small hose take alone?

   15
8. 8.

   Esme's club paints the stage set with two rollers together in 4 hours. The wide roller alone takes 6 hours. How many hours does the narrow roller take alone?

   12
9. 9.

   Kira has 10 cups of punch that is 1/5 orange juice. How many cups of water make it 1/8 orange juice?

   6
10. 10.

    Milo mixes 8 cups of paint that is 1/2 blue. How many cups of white paint make it 2/5 blue?

    2