Question

Rút gọn P

\(P=\dfrac{\sqrt{x}}{\sqrt{x}+5}+\dfrac{2\sqrt{x}}{\sqrt{x}-5}-\dfrac{3x+25}{x-25}\left(x\ge0,x\ne25\right)\)

Answer 1

\(P=\dfrac{x-5\sqrt{x}+2x+10\sqrt{x}-3x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}=\dfrac{5\sqrt{x}-25}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}=\dfrac{5}{\sqrt{x}+5}\)

Answer 2

\(P=\dfrac{\sqrt{x}}{\sqrt{x}+5}+\dfrac{2\sqrt{x}}{\sqrt{x}-5}-\dfrac{3x+25}{x-25}\\ \Leftrightarrow P=\dfrac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}+\dfrac{2\sqrt{x}\left(\sqrt{x}+5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}-\dfrac{3x+25}{\left(\sqrt{x}+5\right)}\\ \Leftrightarrow P=\dfrac{x-5\sqrt{x}+2x+10\sqrt{x}-3x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\\ \Leftrightarrow P=\dfrac{5\sqrt{x}-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\\ \Leftrightarrow P=\dfrac{5\left(\sqrt{x}-5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\)

\(\Leftrightarrow P=\dfrac{5}{\sqrt{x}+5}\)

Answer 3

-> \(\dfrac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}+\dfrac{2\sqrt{x}\left(\sqrt{x}+5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}-\dfrac{3x+25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\)

-> \(\dfrac{x-5\sqrt{x}+2x+10\sqrt{x}-3x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\)

-> \(\dfrac{5\sqrt{x}-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\)

-> \(\dfrac{5\left(\sqrt{x}-5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}\)

-> \(\dfrac{5}{\left(\sqrt{x}+5\right)}\)