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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

4. Arithmetic Series

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Exercise 67 Page 593

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

Simplified Expression: (z+10)(z+2)/z-1
Restrictions: z≠ 0, or z≠ 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.

3z^4+36z^3+60z^2/3z^3-3z^2

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Factor the numerator

Factor out 3z^2

3z^2(z^2+12z+20)/3z^3-3z^2

Write as a sum

3z^2(z^2+2z+10z+20)/3z^3-3z^2

Factor out z

3z^2(z(z+2)+10z+20)/3z^3-3z^2

Factor out 10

3z^2(z(z+2)+10(z+2))/3z^3-3z^2

Factor out (z+2)

3z^2(z+10)(z+2)/3z^3-3z^2

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Factor the denominator

Factor out 3z^2

3z^2(z+10)(z+2)/3z^2(z-1)

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Simplify

CancelCommonFac

Cancel out common factors

3z^2* (z+10)(z+2)/3z^2* (z-1)

Simplify quotient

(z+10)(z+2)/z-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
3z^2	3z^2≠ 0	z≠ 0
z-1	z-1≠ 0	z≠ 1

We found two unique restrictions on the variable. z≠ 0, or z≠ 1

Subchapter links

Lesson Check p.591

Practice and Problem-Solving Exercises p.591-593

Standardized Test Prep p.593

Mixed Review p.593