Add and subtract rational expressions, and simplify complex fractions

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Jun works out 2/(x + 3) + 5/(x − 2) on a worksheet. Which is the answer as one fraction?

   • (7x + 11)/((x + 3)(x − 2))
   • 7/(2x + 1)
   • 7/((x + 3)(x − 2))
2. 2.

   Kira works out 4/(x − 5) + 3/(x + 1) in a notebook. Which is the answer as one fraction?

   • (7x − 11)/((x − 5)(x + 1))
   • 7/((x − 5)(x + 1))
   • 7/(2x − 4)
3. 3.

   Luz works out 6/(x + 4) − 1/(x − 3) in pencil. Which is the answer as one fraction?

   • (7x − 14)/((x + 4)(x − 3))
   • (5x − 14)/((x + 4)(x − 3))
   • 5/((x + 4)(x − 3))
   • (5x − 22)/((x + 4)(x − 3))
4. 4.

   Milo works out 3/(x − 4) − 2/(x + 5) from a math book. Which is the answer as one fraction?

   • (5x + 7)/((x − 4)(x + 5))
   • 1/((x − 4)(x + 5))
   • (x + 23)/((x − 4)(x + 5))
   • (x + 7)/((x − 4)(x + 5))
5. 5.

   Noah adds 1/(x² − 9) + 2/(x² + 5x + 6) on a worksheet. Which is the least common denominator (LCD)?

   • (x − 3)(x + 3)²(x + 2)
   • (x − 3)(x + 3)(x + 2)
   • x + 3
6. 6.

   Pia adds x/(x² − 4x) + 3/(x² − 16) in a notebook. Which is the least common denominator (LCD)?

   • x − 4
   • x(x − 4)²(x + 4)
   • x(x − 4)(x + 4)
7. 7.

   Ren adds 5/(x² + x − 2) + 1/(x² − 1) in pencil. Which is the least common denominator (LCD)?

   • x − 1
   • (x + 2)(x − 1)(x + 1)
   • (x + 2)(x − 1)²(x + 1)
8. 8.

   Tala adds 2/(x² − 6x + 9) + 7/(x² − 9) from a math book. Which is the least common denominator (LCD)?

   • (x − 3)³(x + 3)
   • (x − 3)²(x + 3)
   • x − 3
   • (x − 3)(x + 3)
9. 9.

   Bo simplifies the complex fraction (1 − 25/x²)/(1/x + 5/x²) in pencil. What is it in simplest form?

   x − 5
10. 10.

    Esme simplifies the complex fraction (x + 1 − 6/x)/(1 − 2/x) from a math book. What is it in simplest form?

    x + 3