Question

Rút gọn:

A=\(\dfrac{\sqrt{a}+2}{\sqrt{a+3}}-\dfrac{5}{a+\sqrt{a}-6}+\dfrac{1}{2-\sqrt{a}}\)

B=\((1-\dfrac{\sqrt{a}}{\sqrt{a}+1})\div(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}+\dfrac{\sqrt{a}+2}{3-\sqrt{a}}+\dfrac{\sqrt{a}+2}{a-5\sqrt{a}+6)}\)

C=\((\dfrac{\sqrt{a}-1}{3\sqrt{a}-1}-\dfrac{1}{3\sqrt{a}+1}+\dfrac{8\sqrt{a}}{9a-1})\div(1-\dfrac{3\sqrt{a}-2}{3\sqrt{a}+1)}\)

Giups mình cái mình đag cần gấp

Answer 1

\(A=\dfrac{\sqrt{a}+2}{\sqrt{a}+3}-\dfrac{5}{\left(\sqrt{a}+3\right).\left(\sqrt{a}-2\right)}-\dfrac{1}{\sqrt{a}-2}\)

=\(\dfrac{\left(\sqrt{a}+2\right).\left(\sqrt{a}-2\right)-5-\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{a-4-5-\sqrt{a}-3}{\left(\sqrt{a}+3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{a-\sqrt{a}-12}{\left(\sqrt{a}+3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{\left(\sqrt{a}-4\right).\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{\sqrt{a}-4}{\sqrt{a}-2}\)

Answer 2

Điều kiện bạn tự ghi nhé

\(B=\dfrac{1}{\sqrt{a}+1}:\left(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-3}+\dfrac{\sqrt{a}+2}{\left(\sqrt{a}-3\right).\left(\sqrt{a}-2\right)}\right)\)

\(=\dfrac{1}{\sqrt{a}+1}:\left(\dfrac{\left(\sqrt{a}+3\right).\left(\sqrt{a}-3\right)-\left(\sqrt{a}-2\right).\left(\sqrt{a}+2\right)+\sqrt{a}+2}{\left(\sqrt{a}-3\right).\left(\sqrt{a}-2\right)}\right)\)

\(=\dfrac{1}{\sqrt{a}+1}:\dfrac{a-9-a+4+\sqrt{a}+2}{\left(\sqrt{a}-3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{1}{\sqrt{a}+1}:\dfrac{\sqrt{a}-3}{\left(\sqrt{a}-3\right).\left(\sqrt{a}-2\right)}\)

\(=\dfrac{1}{\sqrt{a}+1}:\dfrac{1}{\sqrt{a}-2}\)

\(=\dfrac{1}{\sqrt{a}+1}.\dfrac{\sqrt{a}-2}{1}=\dfrac{\sqrt{a}-2}{\sqrt{a}+1}\)

Answer 3

Tự ghi ĐKXĐ nhé!

\(C=\left(\dfrac{\left(\sqrt{a}-1\right).\left(3\sqrt{a}+1\right)-\left(3\sqrt{a}-1\right)+8\sqrt{a}}{\left(3\sqrt{a}-1\right).\left(3\sqrt{a}+1\right)}\right):\dfrac{3\sqrt{a}+1-3\sqrt{a}+2}{3\sqrt{a}+1}\)\(=\dfrac{3a-2\sqrt{a}-1-3\sqrt{a}+1+8\sqrt{a}}{\left(3\sqrt{a}-1\right).\left(3\sqrt{a}+1\right)}:\dfrac{3}{3\sqrt{a}+1}\)

\(=\dfrac{3a+3\sqrt{a}}{\left(3\sqrt{a}-1\right).\left(3\sqrt{a}+1\right)}.\dfrac{3\sqrt{a}+1}{3}\)

\(=\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{3\sqrt{a}-1}\)

\(=\dfrac{a+\sqrt{a}}{3\sqrt{a}-1}\)