Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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 - Building Confidence

NameDate

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

Luz solves 4/(x − 5) = 3/(x − 6) in a notebook. What is x?
Milo solves 5/(x − 4) = 2/(x + 5) in pencil. What is x?
Noah solves 6/(x − 3) = 4/(x − 1) from a math book. What is x?
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 only
- x = 4 and x = -4
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?
- x = 3 only
- No solution
- x = 3 and x = -2
- x = -2 only
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?
- No solution
- x = 2 only
- x = -5 only
- x = -5 and x = 2
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?
- No solution
- x = 1 only
- x = 1 and x = -6
- x = -6 only
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(x + 2) = 4
- x + 3 = 4(x + 2)
- x + 3 = 4
- x + 3x + 2 = 4
9.
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 + 4 = 9(x + 1)
- x + 4(x + 1) = 9
- x + 4x + 1 = 9
10.
Jun multiplies every term of x/(x − 3) + 5 = 2/(x − 3) by x − 3 from a math book. Which equation does that give?
- x + 5(x − 3) = 2
- x + 5x − 3 = 2
- x + 5 = 2(x − 3)
- x + 5 = 2

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