Rational expressions

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Rational expressions

  1. State any restrictions on the variables.

    3y² – 3y

    y + 1

  2. Simplify.  Be sure to state the restrictions on the variables

      u² – 4 

    (u – 6)(u – 2)

  3. Multiply.

    5a³  times 2ab

    ab              35

  4. Multiply.

    (a – 4)(a + 3)  times  2a²

    a² – 4a                       (a + 3)(a – 1)

  5. Divide and Simplify

    3x³  divided by x

    4y                     9y

  6. Simplify completely

    4x -12 times x + 3   times 16

    x² – 9            5x² – 25x       x² – 25

  7. Find the least common denominator of the two rational expressions

    4k    +    2

    k² – 9     3 – k

  8. Subtract and simplify

    4x + 1 –  3x – 4

    X – 5      x- 5

  9. Subtract and simplify

    3g – 1 – 1- g

    9             6

  10. Add the rational expressions

    3x – 4 divided by  x

    (x- 3)(x + 2)           x + 2

  11. Subtract and simplify

      4y                –  1 

    y² – 10y + 21      y – 7

  12. Simplify

    x² + 3x + 2

    x + 2

  13. Find the lowest common denominator of the fractions and simplify.  Assume that no denominator equals zero.

    5      –    4

    3x²y      6xy³