Find the least common denominator of the rational expressions. -8 and 10 x² - 25 x( x - 5) A) x( x + 5)( x - 5) B) ( x² + 5)( x² - 5) C) x( x - 5) D) x( x + 5)( x - 5)2

Question

Quizplus · Accepted Answer

The least common denominator (LCD) of the given expressions must account for all the unique factors from each denominator. The denominators, when simplified, are $x^2 - 25$ (which factors into $(x + 5)(x - 5)$) and $x(x - 5)$. The LCD must include each unique factor in its highest power found in any of the denominators, which is $x(x + 5)(x - 5)$, making option A correct.

Find the Least Common Denominator of the Rational Expressions