8.6: Rational Expressions- Answers to the Homework Exercises
- Page ID
- 83243
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Reduce Rational Expressions
- \(3\)
- \(\dfrac{1}{2}\)
- undefined; \(a=-1\) is an excluded value
- \(-10\)
- \(0\)
- \(-8,4\)
- \(0,-10\)
- \(0,-\dfrac{1}{2}\)
- \(\dfrac{3}{5a}\)
- \(\dfrac{3m-4}{10}\)
- \(\dfrac{1}{x+7}\)
- \(\dfrac{n+6}{n-5}\)
- \(\dfrac{2x-7}{5x-7}\)
- \(\dfrac{2n-1}{9}\)
- \(\dfrac{9x}{2}\)
- \(\dfrac{1}{9}\)
- \(\dfrac{7r+8}{8r}\)
- \(\dfrac{3(x-3)}{5x+4}\)
- \(\dfrac{9}{p+2}\)
- \(\dfrac{2(m+2)}{5m-3}\)
- \(\dfrac{7n-4}{4}\)
- \(\dfrac{7a+9}{2(3a-2)}\)
- \(\dfrac{5b-8}{5b+2}\)
- \(\dfrac{7x-6}{(3x+4)(x+1)}\)
Multiply and Divide Rational Expressions
- \(4x^2\)
- \(\dfrac{3x^2}{2}\)
- \(\dfrac{r-6}{r+10}\)
- \(\dfrac{x-10}{7}\)
- \(5\)
- \(\dfrac{4(m-5)}{5m^2}\)
- \(\dfrac{b+2}{8b}\)
- \(\dfrac{1}{a+7}\)
- \(9m^2(m+10)\)
- \(\dfrac{5b}{b+5}\)
- \(\dfrac{14}{3}\)
- \(\dfrac{5p}{2}\)
- \(x+4\)
- \(\dfrac{1}{v-10}\)
- \(\dfrac{p-10}{p-4}\)
- \(7\)
- \(\dfrac{v-9}{5}\)
- \(\dfrac{7}{8(k+3)}\)
- \(\dfrac{10}{9(n+6)}\)
- \(n+3\)
- \(\dfrac{3}{2}\)
- \(\dfrac{1}{a+2b}\)
- \(\dfrac{x-3}{5x+2}\)
- \(\dfrac{x+1}{3x+2}\)
Obtain the Lowest Common Denominator
- \(18\)
- \(6a^2c^3\)
- \(x^2-x-12\)
- \(20xy\)
- \(x^2-2x-3\)
- \(12a^4b^5\)
- \((x+2)(x-4)\)
- \((x+1)(x+2)(x+3)\)
- \(4(x-2)\)
- \((x-3)^2(x+3)\)
- \(\dfrac{6a^4}{10a^3b^2},\:\dfrac{2b}{10a^3b^2}\)
- \(\dfrac{x^2-4x}{(x-4)^2(x+4)},\:\dfrac{3x^2+12x}{(x-4)^2(x+4)}\)
- \(\dfrac{4x}{(x-3)(x+2)},\:\dfrac{x^2+4x+4}{(x-3)(x+2)}\)
- \(\dfrac{5}{x(x-6)},\:\dfrac{2x-12}{x(x-6)},\:\dfrac{-3x}{x(x-6)}\)
- \(\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)},\:\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}\)
Add and Subtract Rational Expressions
- \(\dfrac{6}{a+3}\)
- \(\dfrac{x+6}{x-5}\)
- \(\dfrac{15t+16}{18t^3}\)
- \(\dfrac{-7x-13}{4x}\)
- \(\dfrac{-z^2+5z}{z^2-1}\)
- \(\dfrac{4t-5}{4(t-3)}\)
- \(\dfrac{t^2+2ty-y^2}{y^2-t^2}\)
- \(\dfrac{x-8}{(x+8)(x+6)}\)
- \(\dfrac{2x+4}{x^2+4x+3}\)
- \(\dfrac{a-2}{a^2-9}\)
- \(\dfrac{5(x-1)}{(x+1)(x+3)}\)
- \(x-4\)
- \(\dfrac{3x+4}{x^2}\)
- \(\dfrac{5x+9}{24}\)
- \(\dfrac{-c^2+cd-d^2}{c^2d^2}\)
- \(\dfrac{11x+15}{4x(x+5)}\)
- \(\dfrac{2x+10}{(x+3)^2}\)
- \(\dfrac{2x^2-10x+25}{x(x-5)}\)
- \(\dfrac{2x-5}{(x-3)(x-2)}\)
- \(\dfrac{2x+7}{x^2+5x+6}\)
- \(\dfrac{2}{y^2-y}\)
- \(\dfrac{5x+5}{x^2+2x-15}\)
- \(\dfrac{x+1}{x+2}\)
- \(\dfrac{x-4}{x+2}\)
Compound Rational Expressions
- \(\dfrac{x}{x-1}\)
- \(-\dfrac{a-1}{a+1}\)
- \(-\dfrac{1}{2}\)
- \(\dfrac{x}{3}\)
- \(\dfrac{x-5}{x+9}\)
- \(\dfrac{x-2}{x+2}\)
- \(\dfrac{5-a}{a}\)
- \(\dfrac{4}{5}\)
- \(\dfrac{2a^2-3a+3}{-4a^2-2a}\)
- \(\dfrac{x+2}{x-1}\)
- \(\dfrac{1}{x+4}\)
- \(\dfrac{x-3}{x+4}\)
- \(\dfrac{a-3b}{a+3b}\)
- \(\dfrac{-2a-2}{3a-4}\)
- \(-\dfrac{2x}{x^2+1}\)