Question

13. P= \(\dfrac{x+2}{x\sqrt{x}+1}+\dfrac{\sqrt{x}-1}{x-\sqrt{x}+1}-\dfrac{\sqrt{x}-1}{x-1}\)
a. Rút gọn P
b. Tìm x để \(\left|P\right|\)=\(\dfrac{2}{3}\)
 

Answer 1

a: \(P=\dfrac{x+2+x-1}{x\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\)

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

b: |P|=2/3
mà P>=0

nên P=2/3

=>căn x/(x-căn x+1)=2/3

=>2x-2căn x+2=3căn x

=>2x-5*căn x+2=0

=>(căn x-2)(2căn x-1)=0

=>x=4 hoặc x=1/4