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.

   Kira solves 2/(x − 1) + 3/(x + 1) = 24/(x² − 1) on a worksheet. What is x?

   5
2. 2.

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

   -5
3. 3.

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

   6
4. 4.

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

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

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

   • x = -2
   • No solution
   • x = 4
   • x = -2 and x = 4
6. 6.

   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
7. 7.

   Two leaf blowers clear Jun's school path together in 10 minutes. One alone takes 14 minutes. How many minutes does the other take alone?

   35
8. 8.

   Luz has 12 cups of lemonade that is 1/3 lemon juice. How many cups of water make it 1/4 lemon juice?

   4
9. 9.

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

   2
10. 10.

    Noah has 9 cups of apple drink that is 2/3 apple juice. How many cups of water make it 1/2 apple juice?

    3