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In multiplying rational expressions, we use the following rule:

Multiplying and Dividing Rational Expressions. In multiplying rational expressions, we use the following rule:. Dividing by a rational expression is the same as multiplying by its reciprocal. To multiply rational expressions we use the following steps:.

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In multiplying rational expressions, we use the following rule:

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  1. Multiplying and Dividing Rational Expressions. In multiplying rational expressions, we use the following rule: Dividing by a rational expression is the same as multiplying by its reciprocal.

  2. To multiply rational expressions we use the following steps: • Multiply the numerator and multiply the denominator. • Factor completely the numerator and the denominator. 3. Cancel common factors and simplify

  3. Multiply: Factor 16 and use product rule to multiply. Cancel common factors and simplify

  4. Multiply: Factor numbers on numerator and denominator. Cancel common factors and use quotient rule.

  5. Multiply:

  6. Multiply: Factor numerator Cancel common factors and use quotient rule = 3(a + b)

  7. Divide: Dividing by a rational expression is the same as multiplying by its reciprocal. Change the division to a multiplication and invert the divisor. Factor numbers and use product rule

  8. Cancel common factors Use quotient rule

  9. Divide: Change the division to a multiplication and invert the divisor. Use quotient rule

  10. Divide: Change the division to a multiplication and invert the divisor. Factor each expression

  11. x x +9 -2 x2 + 7x – 18 = (x + 9)(x – 2) x x x2 – 17x + 30 = (x – 15)(x – 2) 3x + 3 = 3(x + 1) -15 -2 Cancel common factors

  12. Divide: Change the division to a multiplication and invert the divisor. Factor common factors. Factor all expressions Cancel common factors

  13. Divide: Change the division to a multiplication and invert the divisor. Factor all expressions. x x x2 – y2 = (x + y) (x – y) - y - y x2 – 2xy + y2 = (x – y) (x – y) = (x – y)2

  14. Cancel common factors

  15. 2x x Multiply: Factor common factors. - 1 - 3 Factor all expressions x x 2x2 – 7x + 3 = (2x – 1) (x – 3) - 1 + 3 x2 + 2x – 3 = (x + 3) (x – 1)

  16. Cancel common factors

  17. r Divide: 3r Change division to multiplication. +2s +5s Factor all expressions 3r 2r - s +5s 3r 2r Cancel common factors -s -s 3r 2r +2s -s

  18. Divide: Change the division to a multiplication. Factor all expressions. r r r2 + r – 6 = (r + 3) (r – 2) +6 - 2 r2 + 4r – 12 = (r + 6) (r – 2) Cancel common factors

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