Question

Rut gon 

a)  ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\))  . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))

b)  \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6

Answer 1

\(a,\)\(\left(2-\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\right).\left(2-\frac{\sqrt{a}\left(b+5\right)}{\sqrt{b}-5}\right).\)

\(=\left(2-\sqrt{a}\right)\left(\frac{2\sqrt{b}-10-\sqrt{ab}-5\sqrt{a}}{\sqrt{b}-5}\right)\)

\(=\left(2-\sqrt{a}\right)\left(\frac{2\left(\sqrt{b}-5\right)-\sqrt{a}\left(\sqrt{b}-5\right)}{\sqrt{b}-5}\right)\)

\(=\frac{\left(2-\sqrt{a}\right)\left(2-\sqrt{a}\right)\left(\sqrt{b}-5\right)}{\sqrt{b}-5}=\left(2-\sqrt{a}\right)^2\)

\(=a-4\sqrt{a}+4\)

Answer 2

\(b,\frac{9-a}{\sqrt{a}+3}-\frac{9-6\sqrt{a}+a}{\sqrt{a}-3}-6\)

\(=\frac{\left(3-\sqrt{a}\right)\left(3+\sqrt{a}\right)}{\sqrt{a}+3}-\frac{\left(\sqrt{a}-3\right)^2}{\sqrt{a}-3}-6\)

\(=3-\sqrt{a}-\left(\sqrt{a}-3\right)-6\)

\(=-2\sqrt{a}\)