Grade 11 · Math · Algebra 2

11th grade Solve rational equations, and check for fake solutions worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Solve rational equations, and check for fake solutions

Grade 11 Math Worksheet

NameDate

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

Kira solves x/(x − 7) + 2 = 13/(x − 7) on a worksheet. What is x?
Luz solves x/(x − 7) + 3 = 3/(x − 7) in a notebook. What is x?
Milo solves 2x/(x − 7) + 2 = 10/(x − 7) in pencil. What is x?
Pia solves x²/(x − 2) = (-5x + 14)/(x − 2) on a worksheet. What are all the solutions?
Ren solves x²/(x + 4) = (x + 20)/(x + 4) in a notebook. What are all the solutions?
Tala solves x²/(x − 6) = (5x + 6)/(x − 6) in pencil. What are all the solutions?
Zee solves x²/(x + 3) = (5x + 24)/(x + 3) from a math book. What are all the solutions?
Two hoses fill Bo's garden barrel. The big hose takes 12 minutes alone and the small hose 24 minutes. How many minutes do both take together?
Esme has two leaf blowers for the school path. One clears it in 10 minutes and the other in 15 minutes. How many minutes do both take together?
Jun's art club paints a mural with two rollers. The wide roller alone takes 3 hours and the narrow one 6 hours. How many hours do both take together?

Solve rational equations, and check for fake solutions. Every version has 10 questions, and the answer key prints on the second page.

I can clear the fractions in an equation by multiplying every term by the common bottom.
I can check each answer and throw out any that makes a bottom 0.
I can solve work and mixture problems with a rational equation.

Standard: A-REI.A.2, A-CED.A.1

rational equation: An equation with x in the bottom of a fraction.

clear the fractions: Multiply every term by the common bottom so no fractions are left.

fake (extraneous) solution: An answer from the cleared equation that makes a bottom 0.

rate of work: The part of a job done in one minute or hour.

Multiplied each top by its own bottom instead of the other one.

Multiplied only the first term inside brackets, so 3(x + 4) became 3x + 4.

Kept an answer that makes a bottom 0, which the equation never allows. Ask your child to put each answer back into the original equation.

Ask: in 2/3 = 4/6, which numbers multiply to check it?

Ask: what is 3 × (x + 4) for x = 1?

What is the most common mistake with solve rational equations, and check for fake solutions?

Multiplied each top by its own bottom instead of the other one.

How can I help my child with solve rational equations, and check for fake solutions?

Ask: in 2/3 = 4/6, which numbers multiply to check it?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records