8.6: Rational Expressions- Answers to the Homework Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Reduce Rational Expressions
- 3
- 12
- undefined; a=−1 is an excluded value
- −10
- 0
- −8,4
- 0,−10
- 0,−12
- 35a
- 3m−410
- 1x+7
- n+6n−5
- 2x−75x−7
- 2n−19
- 9x2
- 19
- 7r+88r
- 3(x−3)5x+4
- 9p+2
- 2(m+2)5m−3
- 7n−44
- 7a+92(3a−2)
- 5b−85b+2
- 7x−6(3x+4)(x+1)
Multiply and Divide Rational Expressions
- 4x2
- 3x22
- r−6r+10
- x−107
- 5
- 4(m−5)5m2
- b+28b
- 1a+7
- 9m2(m+10)
- 5bb+5
- 143
- 5p2
- x+4
- 1v−10
- p−10p−4
- 7
- v−95
- 78(k+3)
- 109(n+6)
- n+3
- 32
- 1a+2b
- x−35x+2
- x+13x+2
Obtain the Lowest Common Denominator
- 18
- 6a2c3
- x2−x−12
- 20xy
- x2−2x−3
- 12a4b5
- (x+2)(x−4)
- (x+1)(x+2)(x+3)
- 4(x−2)
- (x−3)2(x+3)
- 6a410a3b2,2b10a3b2
- x2−4x(x−4)2(x+4),3x2+12x(x−4)2(x+4)
- 4x(x−3)(x+2),x2+4x+4(x−3)(x+2)
- 5x(x−6),2x−12x(x−6),−3xx(x−6)
- 3x2+4x+1(x−4)(x+3)(x+1),2x2−8x(x−4)(x+3)(x+1)
Add and Subtract Rational Expressions
- 6a+3
- x+6x−5
- 15t+1618t3
- −7x−134x
- −z2+5zz2−1
- 4t−54(t−3)
- t2+2ty−y2y2−t2
- x−8(x+8)(x+6)
- 2x+4x2+4x+3
- a−2a2−9
- 5(x−1)(x+1)(x+3)
- x−4
- 3x+4x2
- 5x+924
- −c2+cd−d2c2d2
- 11x+154x(x+5)
- 2x+10(x+3)2
- 2x2−10x+25x(x−5)
- 2x−5(x−3)(x−2)
- 2x+7x2+5x+6
- 2y2−y
- 5x+5x2+2x−15
- x+1x+2
- x−4x+2
Compound Rational Expressions
- xx−1
- −a−1a+1
- −12
- x3
- x−5x+9
- x−2x+2
- 5−aa
- 45
- 2a2−3a+3−4a2−2a
- x+2x−1
- 1x+4
- x−3x+4
- a−3ba+3b
- −2a−23a−4
- −2xx2+1