Question

Cho biểu thức M= \(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right).\dfrac{1}{\sqrt{x}}\)

a) rút gọn M

b) tìm giá trị x để M = \(\dfrac{x}{-3}\)

Answer 1

a) ĐKXĐ: \(x>0,x\ne1\)

\(M=\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right).\dfrac{1}{\sqrt{x}}=\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{1}{\sqrt{x}}\)

\(=\dfrac{-4\sqrt{x}}{x-1}.\dfrac{1}{\sqrt{x}}=-\dfrac{4}{x-1}\)

b) \(M=\dfrac{x}{-3}\Rightarrow\dfrac{-4}{x-1}=\dfrac{x}{-3}\Rightarrow x^2-x=12\Rightarrow x^2-x-12=0\)

\(\Rightarrow\left(x-4\right)\left(x+3\right)=0\) mà \(x>0\Rightarrow x=4\) (thỏa)