Question

Answer 1

a: ĐKXĐ: x<>0; x<>1; x<>-1

\(P=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}:\dfrac{x^2-1+x+2-x^2}{x\left(x-1\right)}\)

\(=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}\cdot\dfrac{x\left(x-1\right)}{x+1}=\dfrac{x^2}{x-1}\)

b: P<1

=>(x^2-x+1)/(x-1)<0

=>x-1<0

=>x<1

=>x<1 và \(x\notin\left\{0;-1\right\}\)

c: \(P=\dfrac{x^2-1+1}{x-1}=x+1+\dfrac{1}{x-1}=x-1+\dfrac{1}{x-1}+2\)

=>\(P>=2\sqrt{\left(x-1\right)\cdot\left(\dfrac{1}{x-1}\right)}+2=4\)

Dấu = xảy ra khi x=2