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Pearson Algebra 2 Common Core, 2011 View details

4. Ellipses

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Exercise 70 Page 644

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

Simplified Expression: x-6/x-1
Restrictions: x≠ - 6, x ≠ 1

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.

x^2-36/x^2+5x-6

▼

Factor the numerator

WritePow

Write as a power

x^2-6^2/x^2+5x-6

FacDiffSquares

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

(x+6)(x-6)/x^2+5x-6

▼

Factor the denominator

WriteDiff

Write as a difference

(x+6)(x-6)/x^2+6x-x-6

FactorOut

Factor out x

(x+6)(x-6)/x(x+6)-x-6

FactorOut

Factor out - 1

(x+6)(x-6)/x(x+6)-1(x+6)

FactorOut

Factor out (x+6)

(x+6)(x-6)/(x+6)(x-1)

▼

Simplify

CancelCommonFac

Cancel out common factors

(x+6)(x-6)/(x+6)(x-1)

SimpQuot

Simplify quotient

x-6/x-1

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.

Denominator	Restrictions on the Denominator	Restrictions on the Variable
(x+6)(x-1)	x+6 ≠ 0 and x-1 ≠ 0	x ≠ - 6 and x ≠ 1
x-1	x-1 ≠ 0	x ≠ 1

We found two unique restrictions on the variable. x≠ - 6 and x ≠ 1

Subchapter links

Lesson Check p.642

Practice and Problem-Solving Exercises p.642-644

Standardized Test Prep p.644

Mixed Review p.644

Exercise 70 Page 644

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