Question

ребята, пожалуйста помогите сократить дроби и решить ​

Answer 1

$б) \: \frac{4 - {x}^{2} }{ {x}^{2} + 3x + 2} = \frac{(2 - x)(2 + x)}{(x - 2)(x - 1)} = \\ = \frac{ - (x - 2)(2 + x)}{(x - 2)(x - 1)} = \frac{ -(2 + x)}{x - 1} = \\ = \frac{2 + x}{1 - x}$

$в) \: \frac{ {x}^{2} + x - 2}{ {x}^{2} - 5x + 4} = \frac{(x + 2)(x - 1)}{(x - 4)(x - 1)} = \frac{x + 2}{x - 4}$

$д) \: \frac{2 {x}^{2} + 5x - 3 }{4 {x}^{2} + 11x - 3} = \frac{2(x - 0.5)(x + 3)}{4(x - 0.25)(x + 3)} = \\ = \frac{x - 0.5}{2x - 0.5}$

$1) \: 2 {x}^{2} + 5x - 3 = 0 \\ x = \frac{ - 5 + \sqrt{25 + 4 \times 3 \times 2} }{2 \times 2} = \\ = \frac{ - 5 + \sqrt{49} }{4} = \frac{ - 5 + 7}{4} \\ x = \frac{ - 5 - 7}{4} = \frac{ - 12}{4} = - 3 \\ x = \frac{ - 5 + 7}{4} = \frac{2}{4} = 0.5$

$2) \: 4 {x}^{2} + 11x - 3 = 0 \\ x = \frac{ - 11 + \sqrt{121 + 16 \times 3} }{8} = \\ = \frac{ - 11 + 13}{8} \\ x = \frac{ - 11 - 13}{8} = - 3 \\ x = \frac{ - 11 +1 3}{8} = \frac{2}{8} = 0.25$