Question

A=\(\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right)\div\dfrac{1}{x-\sqrt{x}}\)

a,rút gọn A

b,tìm x để A=5

Answer 1

a: ĐKXĐ: x>0 và x<>1

\(A=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{1}{x-\sqrt{x}}\)

\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{1}{\left(\sqrt{x}-1\right)\cdot\sqrt{x}}\)

\(=\dfrac{1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{1}\)

\(=\sqrt{x}+1\)

b: A=5

=>\(\sqrt{x}+1=5\)

=>\(\sqrt{x}=4\)

=>x=16(nhận)