Question

\(\frac{5}{a+1}-\frac{10}{a-\left(a^2+1\right)}-\frac{15}{a^3+1}\)

Answer 1

\(\dfrac{5}{a+1}+\dfrac{10}{a^2-a+1}-\dfrac{15}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5\left(a^2-a+1\right)+10\left(a+1\right)-15}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a^2-5a+5+10a+10-15}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a^2+5a}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a\left(a+1\right)}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a}{\left(a^2-a+1\right)}\)