Find the least common denominator of the rational expressions.
-$\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }$ and $\frac { 1 } { x ^ { 2 } + x }$
A) $x + 1$
B) $( x + 1 ) ^ { 2 }$
C) $x ( x + 1 ) ^ { 2 }$
D) $x ( x + 8 ) ( x + 1 )$

Question

Quizplus · Accepted Answer

To find the least common denominator (LCD) of the given rational expressions, factor each denominator completely. The first denominator $x^2 + 9x + 8$ factors into $(x + 1)(x + 8)$. The second denominator $x^2 + x$ factors into $x(x + 1)$. The LCD must include each factor the greatest number of times it occurs in any one expression's denominator. Thus, the LCD is $x(x + 8)(x + 1)$, which is option D.

Find the Least Common Denominator of the Rational Expressions x−1x2+9x+8\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }x2+9x+8x−1​

Find the Least Common Denominator of the Rational Expressions $\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }$