Question

A=$\frac{\sqrt{x}+15}{x-9}-\frac{x}{x-3\sqrt{x}}+\frac{2\sqrt{x}+5}{\sqrt{x}+3}$; B=$\frac{\sqrt{x}-3}{14}$
biết  A= căn x / (căn x ) +3
b,Tìm x để A=2B

Answer 1

b: A=2B

=>\(\dfrac{\sqrt{x}}{\sqrt{x}+3}=\dfrac{2\left(8\sqrt{x}-3\right)}{14}=\dfrac{8\sqrt{x}-3}{7}\)

=>\(\left(8\sqrt{x}-3\right)\left(\sqrt{x}+3\right)=7\sqrt{x}\)

=>\(8x+24\sqrt{x}-3\sqrt{x}-9-7\sqrt{x}=0\)

=>\(8x+14\sqrt{x}-9=0\)

=>\(\left(4\sqrt{x}+9\right)\left(2\sqrt{x}-1\right)=0\)

=>\(2\sqrt{x}-1=0\)

=>\(\sqrt{x}=\dfrac{1}{2}\)

=>\(x=\dfrac{1}{4}\left(nhận\right)\)