Question

\(K=\dfrac{\sqrt x-11}{x+2\sqrt x-3}+\dfrac{3\sqrt x}{1-\sqrt x}-\dfrac {2\sqrt x+3}{\sqrt x+3}\)

Rút gọn K

Tìm x khi K=1/2

Tìm x để K có nghĩa

Answer 1

a: \(K=\dfrac{\sqrt{x}-11-3x-9\sqrt{x}-\left(2x-2\sqrt{x}+3\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-3x-8\sqrt{x}-11-2x-\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-5x-9\sqrt{x}-8}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

b: Để K=1/2 thì \(\dfrac{-5x-9\sqrt{x}-8}{x+2\sqrt{x}-3}=\dfrac{1}{2}\)

=>\(-10x-18\sqrt{x}-16=x+2\sqrt{x}-3\)

=>-11x-20căn x+13=0

=>\(x=\left(\dfrac{-10+9\sqrt{3}}{11}\right)^2\)