a) A = ( \(\frac{x+1}{x-1}\)\(-\)\(\frac{x-1}{x+1}\)) \(\div\)\(\frac{2x}{5x-5}\)
= ( \(\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}\)\(-\)\(\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\)) \(\div\)\(\frac{2x}{5x-5}\)
= \(\frac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\)\(\div\)\(\frac{2x}{5x-5}\)
= \(\frac{\left(x+1-x+1\right)\left(x+1+x-1\right)}{\left(x-1\right)\left(x+1\right)}\)\(\times\)\(\frac{5\left(x-1\right)}{2x}\)
= \(\frac{4x}{\left(x-1\right)\left(x+1\right)}\)\(\times\)\(\frac{5\left(x-1\right)}{2x}\)
= \(\frac{10}{x+1}\)