((r+10)/r)+(r/(r+10))
To simplify the expression ((r+10)/r) + (r/(r+10)), we need to find a common denominator for the two fractions and combine them.
Step 1: Find the common denominator.
The denominator of the first fraction is r, and the denominator of the second fraction is (r+10). The common denominator for both fractions is r * (r+10).
Step 2: Adjust the numerators.
To adjust the numerators, we need to multiply each numerator by the factor that will make the denominators equal to the common denominator.
For the first fraction:
Multiply the numerator (r+10) by (r+10)/(r+10) to get (r+10)^2.
For the second fraction:
Multiply the numerator r by r/r to get r^2.
Step 3: Combine the fractions.
After adjusting the numerators, we can now combine the fractions:
((r+10)^2 + r^2) / (r * (r+10))
Step 4: Simplify the expression if possible.
To simplify further, we can expand the numerator using the FOIL method for the square of a binomial:
(r^2 + 2r*10 + 10^2 + r^2) / (r * (r+10))
Simplifying the numerator, we get:
(2r^2 + 20r + 100) / (r * (r+10))
So, the simplified form of the expression ((r+10)/r) + (r/(r+10)) is:
(2r^2 + 20r + 100) / (r * (r+10))