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Reduce (2x² - 18)/(4x² - 4x - 48) to lowest terms

by Timothy
(Mount Clemens, MI)











































I need to understand how to Reduce (2x^2 - 18)/(4x^2 - 4x - 48) to lowest terms.

Comments for Reduce (2x² - 18)/(4x² - 4x - 48) to lowest terms

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Jul 26, 2011
Simplify Algebraic Expression
by: Staff


The question:

by Timothy
(Mount Clemens, MI)

I need to understand how to Reduce (2x^2 - 18)/(4x^2 - 4x - 48) to lowest terms.


The answer:

How to approach this problem:

To simplify this expression, approach it the same way you would use to simplify a fraction using arithmetic.

For example, suppose you wanted to simplify the fraction 6/12.

First, factor both the numerator and denominator. Second, cancel common terms.

6/12

Factor both the numerator and denominator

= (1*2*3)/(1*2*2*3)

Cancel common terms

= [1/(1*2)] *[(2)/(2)]*[(3)/(3)]

= (1/2) * 1 * 1

= (1/2)

6/12 = 1/2



Apply the same approach to the algebraic expression:

(2x² - 18)/(4x² - 4x - 48)


Factor both the numerator and denominator


= [2(x² - 9)]/[(4x² - 4x - 48)]

= [1*2*(x-3)*(x+3)]/[(4x² - 4x - 48)]

= [1*2*(x-3)*(x+3)]/[4(x² - x - 12)]

= [1*2*(x-3)*(x+3)]/[(1*2*2*(x-4)*(x+3)]


Cancel common terms

= [1/(1*2)] * [2/2] * [(x-3)/(x-4)] * [(x+3)/(x+3)]

= [1/2] * 1*[(x-3)/(x-4)] * 1

= [1/2] * [(x-3)/(x-4)]

= [1*(x-3)]/[2*(x-4)]

= (x-3)/[2(x-4)]



The final answer is:

(2x² - 18)/(4x² - 4x - 48) = (x-3)/[2(x-4)]

or, if you prefer:

(2x² - 18)/(4x² - 4x - 48) = (x-3)/(2x-8)






Thanks for writing.

Staff
www.solving-math-problems.com


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