a: ĐKXĐ: \(\left\{{}\begin{matrix}a>=0\\a\ne25\end{matrix}\right.\)
\(A=\left(3+\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(3-\dfrac{a-5\sqrt{a}}{\sqrt{a}-5}\right)\)
\(=\left(3+\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\left(3-\sqrt{a}\cdot\dfrac{\left(\sqrt{a}-5\right)}{\sqrt{a}-5}\right)\)
\(=\left(3+\sqrt{a}\right)\left(3-\sqrt{a}\right)=9-a\)
b: ĐKXĐ: x>=0 và x<>1
\(B=\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x-1}-\dfrac{1}{\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)-2\sqrt{x}-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\cdot\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+\sqrt{x}-3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)
c: ĐKXĐ: a>=0 và a<>1
\(P=\left(1+\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(1-\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\right)\)
\(=\left(1+\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\left(1+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1+\sqrt{a}\right)=a+2\sqrt{a}+1\)
