Question

Сократите дробь х²-3х+2/2х²-5х+2, разложив квадратный трехчлен на множители.​

Answer 1

$\frac{ {x}^{2} - 3x + 2}{2 {x}^{2} - 5x + 2} ; \\ {x}^{2} - 3x + 2 = 0; \\ x {\tiny \: 1,2} = \frac{3 \pm \: \sqrt{9 - 4 \times 1 \times 2} }{2} ; \: \: \: \Rightarrow \\ \Rightarrow \: x {\tiny1} = \frac{3 + 1}{2} = 2; \: \: \: \: \: \: \: \: \: x {\tiny \: 2} = \frac{3 - 1}{2} ; \Rightarrow \\ \Rightarrow \: \underbrace{ {x}^{2} - 3x + 2} _{ \large \: \bigg(x - 2 \bigg) \bigg(x - 1 \bigg)}. \\ \\ 2 {x}^{2} - 5x + 2 = 0; \\ x {\tiny \: 1,2} = \frac{5 \pm \: \sqrt{25 - 4 \times 2 \times 2} }{4} ;\Rightarrow \\ \Rightarrow \: x {\tiny \: 1} \: = \frac{5 + 3}{4} = 2; \: \: \: \: \: \: \: \: \: \: x {\tiny \: 2} = \frac{5 - 3}{4} = \frac{1}{2} ; \Rightarrow \\ \Rightarrow \: \underbrace{2 {x}^{2} - 5x + 2} _{ \large \: 2 \bigg(x - 2 \bigg) \bigg(x - \frac{1}{2} \bigg); \Rightarrow}\\\Rightarrow\underbrace{ \frac{ {x}^{2} - 3x + 2}{2 {x}^{2} - 5x + 2}} _{ \large \: \frac{ \bigg(x - 2 \bigg) \bigg(x - 1 \bigg)}{ \: 2 \bigg(x - 2 \bigg) \bigg(x - \frac{1}{2} \bigg)} = \frac{x - 1}{2x - 1} ; } \\ \boxed{ \huge \it \: \underline{otvet : \Huge \: \frac{x - 1}{2x - 1} }}.$