Question: Simplify (1)/((a+1)(a+2))-(1)/((a+2)(a+3))+(1)/((a+1)(a+3)).
Our expression is: E = T1 - T2 + T3, where
T1 = 1/(a+1)(a+2) = (a+3)/(a+1)(a+2)(a+3)
T2 = 1/(a+2)(a+3) = (a+1)/(a+1)(a+2)(a+3)
T3 = 1/(a+1)(a+3) = (a+2)/(a+1)(a+2)(a+3)
Now that the three terms all have the same denominator, we can simply add together the numerators
E = N/D
where D = (a+1)(a+2)(a+3)
and N = (a+3) - (a+1) + (a+2) = a + 4
Answer: E = N/D = (a+4)/(a+1)(a+2)(a+3)