Question

Find the least common denominator for these two rational expressions.

s^3/s^2+2s+1 and 4/s^2+6s+5

Answer 1

can someone help.

Answer 2

Try factoring the denominators

Answer 3

hmmm actaully one sec.. the 2nd one is off =)

Answer 4

\(\large {\cfrac{s^3}{s^2+2s+1}\quad \cfrac{4}{s^2+6s+5}
\\ \quad \\
hint:\quad
\begin{array}{lllllll}
s^2&+2s&+1&\quad &s^2&+6s&+5\\
&\uparrow&\uparrow &&&\uparrow&\uparrow\\
&1+1&1\cdot 1&&&5+1&5\cdot 1
\end{array}
}\)

factor them out, see what you get

Answer 5

(s+1)^2 and (s+5)(s+1)

Answer 6

yeap thus \(\bf \cfrac{s^3}{s^2+2s+1}\quad \cfrac{4}{s^2+6s+5}\implies \cfrac{s^3}{(s+1)(s+1)}\quad \cfrac{4}{(s+5)(s+1)}
\\ \quad \\
LCD\implies (s+1)(s+1)(s+5)\)

since the (s+1) is already included, from the 1st denominator, it can be skipped for the 2nd, thus

Answer 7

but (s+1) has to be included twice, so it can divide the \((s+1)^2\) denominator