Answer:
The common denominator for 2/5a+10 and 3/a^2+2a is 5a^2+10a.
Explanation:
To find the common denominator, we need to find the least common multiple of the denominators 5a+10 and a^2+2a. The least common multiple of these two denominators is:
LCM(5a+10, a^2+2a) = (5*a^2)*(a+2) = 5a^2+10a
We can find the least common multiple by factoring the denominators and then finding the least common multiple of the factors. The denominator 5a+10 can be factored as 5*(a+2). The denominator a^2+2a can be factored as a(a+2).
The least common multiple of the factors of 5a+10 and a^2+2a is (5a^2)(a+2). This is equal to 5a^2+10a.
Therefore, the common denominator for 2/5a+10 and 3/a^2+2a is 5a^2+10a.