Exercise 7 Page 964

Factor each denominator and numerator as much as you can and cancel out common factors.

Practice makes perfect

We want to multiply the given rational expressions. x^3/x^2-4 * 5x+10/10x We will start by factoring the denominators and numerators, if possible. Let's start with the first expression.

x^3/x^2-4

Factor out x

x* x^2/x^2-4

Rewrite 4 as 2^2

x* x^2/x^2-2^2

a^2-b^2=(a+b)(a-b)

x* x^2/(x+2)(x-2)

Now, let's factor the second expression.

5x+10/10x

Factor out 5

5(x+2)/5(2x)

Cancel out common factors

5(x+2)/5(2x)

Simplify quotient

(x+2)/2x

Now that both expressions have been factored, we will cancel out any common factors.

x* x^2/(x+2)(x-2)*(x+2)/2x

Cancel out common factors

x * x^2/(x+2)(x-2)*(x+2)/2x

Simplify quotient

x^2/(x-2)* 1/2

Multiply fractions

x^2/(x-2)2

Commutative Property of Multiplication

x^2/2(x-2)

This corresponds to option B.

Exercises p.964-971

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