### About Adding & Subtracting Rational Expressions:

When we add or subtract rational expressions, we follow the same procedures we used with fractions. To add or subtract rational expressions, we must first obtain a common denominator. We then add or subtract numerators and place the result over the common denominator. Lastly, we factor numerator and denominator, cancel any common factors, and report a simplified answer.

Test Objectives

- Demonstrate the ability to find the LCD for a group of rational expressions
- Demonstrate the ability to add rational expressions
- Demonstrate the ability to subtract rational expressions

#1:

Instructions: Perform each indicated operation.

a) $$\frac{7}{2p + 2} + \frac{p + 5}{7}$$

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#2:

Instructions: Perform each indicated operation.

a) $$\frac{b + 8}{b^2 + 7b + 10} + \frac{b - 3}{b + 5}$$

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#3:

Instructions: Perform each indicated operation.

a) $$\frac{2x}{x + 1} - \frac{3x}{4x + 4} - \frac{2}{x^2 - 1}$$

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#4:

Instructions: Perform each indicated operation.

a) $$\frac{2x}{2x^2 + 6x} + \frac{2}{x + 3}$$

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#5:

Instructions: Perform each indicated operation.

a) $$\frac{3}{x + 2} + \frac{4}{x^2 - 2x +4} - \frac{13}{x^3 + 8}$$

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Written Solutions:

#1:

Solutions:

a) $$\frac{2p^2 + 12p + 59}{14(p + 1)}$$

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#2:

Solutions:

a) $$\frac{b^2 + 2}{(b + 5)(b + 2)}$$

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#3:

Solutions:

a) $$\frac{5x^2 - 5x - 8}{4(x + 1)(x - 1)}$$

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#4:

Solutions:

a) $$\frac{3}{x + 3}$$

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#5:

Solutions:

a) $$\frac{3x^2 - 2x + 7}{(x+2)(x^2 -2x + 4)}$$