\(\frac{x^2-3x+9}{2x-3}>2\Leftrightarrow\frac{x^2-3x+9}{2x-3}-2>0\)
\(\Leftrightarrow\frac{x^2-3x+9-4x+6}{2x-3}>0\Leftrightarrow\frac{x^2-7x+15}{2x-3}>0\)
\(\Rightarrow2x-3>0\Leftrightarrow x>\frac{3}{2}\)vì \(x^2-7x+15=x^2-2.\frac{7}{2}+\frac{49}{4}+\frac{11}{4}=\left(x-\frac{7}{2}\right)^2+\frac{11}{4}>0\)
\(\frac{x^2-3x+9}{2x-3}>2\)
\(\frac{x^2-3x+9}{2x-3}-2>0\)
\(\frac{x^2-3x+9-4x+6}{2x-3}>0\)
\(\frac{x^2-7x+15}{2x-3}>0\)
ta có \(x^2-7x+15\)
\(\left(x+\frac{7}{2}\right)^2+\frac{11}{4}>0\)
để \(\frac{x^2-7x+15}{2x-3}\)
\(< =>2x-3>0\)
\(x>\frac{3}{2}\)
x<\(\frac{3}{2}\)
ai giải giúp em mấy bài toán này vs ạ giải chi tiết giúp em ạ
