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Mathematics LibreTexts

8.6: Rational Expressions- Answers to the Homework Exercises

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Reduce Rational Expressions

  1. 3
  1. 12
  1. undefined; a=1 is an excluded value
  1. 10
  1. 0
  1. 8,4
  1. 0,10
  1. 0,12
  1. 35a
  1. 3m410
  1. 1x+7
  1. n+6n5
  1. 2x75x7
  1. 2n19
  1. 9x2
  1. 19
  1. 7r+88r
  1. 3(x3)5x+4
  1. 9p+2
  1. 2(m+2)5m3
  1. 7n44
  1. 7a+92(3a2)
  1. 5b85b+2
  1. 7x6(3x+4)(x+1)

Multiply and Divide Rational Expressions

  1. 4x2
  1. 3x22
  1. r6r+10
  1. x107
  1. 5
  1. 4(m5)5m2
  1. b+28b
  1. 1a+7
  1. 9m2(m+10)
  1. 5bb+5
  1. 143
  1. 5p2
  1. x+4
  1. 1v10
  1. p10p4
  1. 7
  1. v95
  1. 78(k+3)
  1. 109(n+6)
  1. n+3
  1. 32
  1. 1a+2b
  1. x35x+2
  1. x+13x+2

Obtain the Lowest Common Denominator

  1. 18
  1. 6a2c3
  1. x2x12
  1. 20xy
  1. x22x3
  1. 12a4b5
  1. (x+2)(x4)
  1. (x+1)(x+2)(x+3)
  1. 4(x2)
  1. (x3)2(x+3)
  1. 6a410a3b2,2b10a3b2
  1. x24x(x4)2(x+4),3x2+12x(x4)2(x+4)
  1. 4x(x3)(x+2),x2+4x+4(x3)(x+2)
  1. 5x(x6),2x12x(x6),3xx(x6)
  1. 3x2+4x+1(x4)(x+3)(x+1),2x28x(x4)(x+3)(x+1)

Add and Subtract Rational Expressions

  1. 6a+3
  1. x+6x5
  1. 15t+1618t3
  1. 7x134x
  1. z2+5zz21
  1. 4t54(t3)
  1. t2+2tyy2y2t2
  1. x8(x+8)(x+6)
  1. 2x+4x2+4x+3
  1. a2a29
  1. 5(x1)(x+1)(x+3)
  1. x4
  1. 3x+4x2
  1. 5x+924
  1. c2+cdd2c2d2
  1. 11x+154x(x+5)
  1. 2x+10(x+3)2
  1. 2x210x+25x(x5)
  1. 2x5(x3)(x2)
  1. 2x+7x2+5x+6
  1. 2y2y
  1. 5x+5x2+2x15
  1. x+1x+2
  1. x4x+2

Compound Rational Expressions

  1. xx1
  1. a1a+1
  1. 12
  1. x3
  1. x5x+9
  1. x2x+2
  1. 5aa
  1. 45
  1. 2a23a+34a22a
  1. x+2x1
  1. 1x+4
  1. x3x+4
  1. a3ba+3b
  1. 2a23a4
  1. 2xx2+1

8.6: Rational Expressions- Answers to the Homework Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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