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Perform the indicated operations. Assume that no denominator has a value of 0.

5m/m+1÷25m^2/m^2+2m+1

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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.

User Akshay Gundewar
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