Find the least common denominator.
-$\frac { 1 } { r ^ { 2 } + 10 r + 25 } - \frac { 1 } { r ^ { 2 } + 5 r }$
A) $( r + 5 ) ^ { 2 }$
B) $r ( r + 5 ) ^ { 2 }$
C)r(r + 1)(r + 5)
D)r(r + 5)

Question

Quizplus · Accepted Answer

The least common denominator (LCD) must account for all factors present in both denominators. Factor each denominator: $r^2 + 10r + 25 = (r + 5)^2$ and $r^2 + 5r = r(r + 5)$. The LCD is $r(r + 5)^2$, which includes both the $r$ and $(r + 5)^2$ factors.

Find the Least Common Denominator 1r2+10r+25−1r2+5r\frac { 1 } { r ^ { 2 } + 10 r + 25 } - \frac { 1 } { r ^ { 2 } + 5 r }r2+10r+251​−r2+5r1​

Find the Least Common Denominator $\frac { 1 } { r ^ { 2 } + 10 r + 25 } - \frac { 1 } { r ^ { 2 } + 5 r }$