Question

a, \(\dfrac{1}{a+1}+\dfrac{2}{1-a}+\dfrac{5a-1}{a^2-1}\)         b, \(\dfrac{1}{9x-18}+\dfrac{16-7x}{72-18x}+\dfrac{5}{12x-24}\)

Answer 1

\(a.\dfrac{1}{a+1}+\dfrac{2}{1-a}+\dfrac{5a-1}{a^2-1}\)

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

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

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

\(=\dfrac{4a-4}{\left(a+1\right)\left(a-1\right)}\)

\(=\dfrac{4}{a+1}\)