`C=(a+2sqrta+1)/(a-1)-sqrta/(a-sqrta)(a>0,a ne 1)`
`=(sqrta+1)^2/((sqrta-1)(sqrta+1))-(sqrta)/(sqrta(sqrta-1))`
`=(sqrta+1)/(sqrta-1)-1/(sqrta-1)`
`=sqrta/(sqrta-1)`
\(C=\dfrac{a+2\sqrt{a}+1}{a-1}-\dfrac{\sqrt{a}}{a-\sqrt{a}}=\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\)
\(=\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}-1}=\dfrac{\sqrt{a}}{\sqrt{a}-1}\)
C=\(\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{1}{\sqrt{a}-1}=\dfrac{\sqrt{a}}{\sqrt{a}-1}\)
