### About Rational Equations:

When we solve an equation with rational expressions, we first clear the denominators. We do this by multiplying both sides of the equation by the LCD. Once this is done, we solve the equation. We must check each proposed solution, to ensure it is not a restricted value in the original equation.

Test Objectives

- Demonstrate the ability to find the LCD for a group of rational expressions
- Demonstrate the ability to solve an equation with rational expressions
- Demonstrate the ability to check the proposed solution(s) for an equation with rational expressions

#1:

Instructions: Solve each equation.

a) $$\frac{3}{x - 1} = \frac{x+5}{2x^2 - 2x} - \frac{5x-10}{x}$$

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#2:

Instructions: Solve each equation.

a) $$1 - \frac{4}{x^2 + 4x} = \frac{x+2}{x+4}$$

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#3:

Instructions: Solve each equation.

a) $$\frac{n - 1}{n + 5} = \frac{1}{n^2+n-20} + \frac{n+3}{n^2+n-20}$$ $$\frac{n - 1}{n + 5} = \frac{1}{n^2+n-20} + $$$$\frac{n+3}{n^2+n-20}$$

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#4:

Instructions: Solve each equation.

a) $$\frac{4}{m + 1} + \frac{m}{m - 5} = 4$$

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#5:

Instructions: Solve each equation.

a) $$\frac{1}{r^2-5r+6} + 1 = \frac{r}{r-3}$$

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Written Solutions:

#1:

Solutions:

a)

x = | 3 |

2 |

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#2:

Solutions:

a) x = 2

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#3:

Solutions:

a) n = 0 or n = 6

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#4:

Solutions:

a) m = 0 or m = 7

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#5:

Solutions:

a)

r = | 7 |

3 |