To perform the indicated operations, we need to simplify the expression by finding a common denominator and then performing the division.
First, let's find the LCD of the fractions in the expression. The denominators of the first fraction is m+1, and the denominator of the second fraction is m^2+2m+1, which can be factored as (m+1)^2. The LCD is therefore (m+1)^2.
Next, we need to rewrite the fractions with the LCD as the denominator. Note that we can rewrite 5m as (m+1)(5), so we have:
[(m+1)(5)]/[(m+1)^2] ÷ 25m^2/[(m+1)^2]
Now we can perform the division by multiplying by the reciprocal of the second fraction:
[(m+1)(5)]/[(m+1)^2] * [(m+1)^2]/25m^2
Canceling out the common factor of (m+1)^2 in the numerator and denominator, we get:
5/25m^2
Simplifying this fraction by factoring out the common factor of 5, we get:
1/5m^2
Therefore, the final simplified expression is 1/5m^2.