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.

   Pia solves 1/(x − 2) + 1/(x + 2) = 4/(x² − 4) on a worksheet. Which describes the solutions?

   • x = -2
   • x = 2
   • No solution
   • Every number
4. 4.

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

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

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

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

   Two printers print Ari's club flyers together in 12 minutes. The fast printer alone takes 20 minutes. How many minutes does the slow printer take alone?

   30
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