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Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
4. Rational Expressions
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Exercise 52 Page 533

Factor each denominator and numerator as much as you can and cancel out common factors. The denominator cannot be zero.

C

Practice makes perfect

We want to multiply the given rational expressions. x/x^2-2x-3 * 2x-6/x^2-4x+3 We will start by factoring the numerators and denominators, if possible. Let's start with the first expression.

x/x^2-2x-3
â–¼
Factor the denominator
WriteDiff

Write as a difference

x/x^2+x-3x-3
FactorOut

Factor out x

x/x(x+1)-3x-3
FactorOut

Factor out -3

x/x(x+1)-3(x+1)
FactorOut

Factor out (x+1)

x/(x+1)(x-3)

Now, let's factor the second expression.

2x-6/x^2-4x+3
â–¼
Factor the numerator
FactorOut

Factor out 2

2(x-3)/x^2-4x+3
â–¼
Factor the denominator
WriteDiff

Write as a difference

2(x-3)/x^2-x-3x+3
FactorOut

Factor out x

2(x-3)/x(x-1)-3x+3
FactorOut

Factor out - 3

2(x-3)/x(x-1)-3(x-1)
FactorOut

Factor out (x-1)

2(x-3)/(x-1)(x-3)

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

x/(x+1)(x-3) * 2(x-3)/(x-1)(x-3)
CancelCommonFac

Cancel out common factors

x/(x+1)(x-3) * 2(x-3)/(x-1)(x-3)
SimpQuot

Simplify quotient

x* 2/(x+1)(x-1)(x-3)
CommutativePropMult

Commutative Property of Multiplication

2x/(x-1)(x+1)(x-3)

The obtained expression corresponds to the Option C.

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