Question

Answer 1

1: \(x^2-7x+6<0\)

=>(x-1)(x-6)<0

=>1<x<6

2: ĐKXĐ: x<>-1

\(\frac{x^2+2x-3}{x+1}\ge0\)

=>\(\frac{\left(x+3\right)\left(x-1\right)}{x+1}\ge0\)

Đặt x+3=0

=>x=-3

Đặt x-1=0

=>x=1

Đặt x+1=0

=>x=-1

Đặt \(f\left(x\right)=\frac{\left(x+3\right)\left(x-1\right)}{\left(x+1\right)}\)

Bảng xét dấu:

Theo bảng xét dấu, ta có: f(x)>=0 khi -3<=x<-1 hoặc x>=1

3:

ĐKXĐ: x<>2

\(\frac{1}{x-2}\ge3\)

=>\(\frac{1}{x-2}-3\ge0\)

=>\(\frac{1-3x+6}{x-2}\ge0\)

=>\(\frac{-3x+7}{x-2}\ge0\)

=>\(\frac{3x-7}{x-2}\le0\)

=>2<x<=7/3