# 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

 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