Exercise 69 Page 644

Factor the numerator and denominator as much as possible. Cancel out common factors, if possible.

Simplified Expression: 1/2x-3x^4

Restrictions: x ≠ 0, x ≠ sqrt(2/3)

Practice makes perfect

We want to simplify the given rational expression. To do so, we will factor the numerator and denominator as much as possible. Then, we will cancel out any common factors.

3x/6x^2-9x^5

FactorOut

Factor out 3x

3x/3x(2x-3x^4)

CancelCommonFac

Cancel out common factors

3x/3x(2x-3x^4)

SimpQuot

Simplify quotient

1/2x-3x^4

We simplified the given expression. Finally, we will identify the restrictions on the variables from the denominator of the simplified expression and from any other denominator used. For simplicity, we will use their factored forms.

1/2x-3x^4

FactorOut

Factor out x

1/x(2-3x^3)

Let's do it!

Denominator	Restrictions on the Denominator	Restrictions on the Variable
3x^2(2-3x^3)	x ≠ 0, 2-3x^3 ≠ 0	x ≠ 0, x ≠ sqrt(2/3)
x(2-3x^3)	x ≠ 0, 2-3x^3 ≠ 0	x ≠ 0, x ≠ sqrt(2/3)

We found two unique restrictions on the variable. x ≠ 0, x ≠ sqrt(2/3)

Subchapter links

Lesson Check p.642

Practice and Problem-Solving Exercises p.642-644

Standardized Test Prep p.644

Mixed Review p.644

Exercise 69 Page 644

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