a: \(A=\dfrac{x+3\sqrt{x}+2-\left(x-4\sqrt{x}+4\right)-12}{x-4}\)
\(=\dfrac{x+3\sqrt{x}-10-x+4\sqrt{x}-4}{x-4}\)
\(=\dfrac{7\sqrt{x}-14}{x-4}=\dfrac{7}{\sqrt{x}+2}\)
b: \(B=\left(\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)-x-9\sqrt{x}}{x-9}\right)\cdot\dfrac{x-25}{\sqrt{x}\left(\sqrt{x}+5\right)}\)
\(=\dfrac{2x+6\sqrt{x}-x-9\sqrt{x}}{x-9}\cdot\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}\cdot\dfrac{\sqrt{x}-5}{\sqrt{x}}=\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\)
a.\(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+2}+\dfrac{12}{4-x}\)
\(ĐK:x\ge0;x\ne4\)
\(A=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}-2\right)-12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(A=\dfrac{x+2\sqrt{x}+\sqrt{x}+2-\left(x-4\sqrt{x}+4\right)-12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(A=\dfrac{x+2\sqrt{x}+\sqrt{x}+2-x+4\sqrt{x}-4-12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(A=\dfrac{7\sqrt{x}+14}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(A=\dfrac{7\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(A=\dfrac{7}{\sqrt{x}-2}\)
b.\(B=\left(\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{x+9\sqrt{x}}{x-9}\right):\dfrac{x+5\sqrt{x}}{x-25}\)
\(ĐK:x\ge0;x\ne25;x\ne9\)
\(B=\left(\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)-\left(x+9\sqrt{x}\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right).\dfrac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\sqrt{x}\left(\sqrt{x}+5\right)}\)
\(B=\left(\dfrac{2x+6\sqrt{x}-x-9\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right).\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
\(B=\dfrac{x-3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
\(B=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x}-5}{\sqrt{x}}\)
\(B=\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\)
