Сократите дробь :1) a^2+5a+6/a^2+4a+4 2) x^2+3x+2/x^2+6x+5 3) m^2+2m+1/m^2+8m+7

1) [latex] \frac{ a^{2} + 5a + 6}{a^{2} + 4a + 4} [/latex] a² + 5a + 6 = 0 D = 5² - 4 * 6 * 1 = 25 - 24 = 1 a₁ = (-5 + √1) / 2*1 = (-5 + 1) / 2 = -4 / 2 = -2 a₂ = (-5 - √1) / 2*1 = (-5 - 1) / 2 = -6 / 2 = -3 a² + 5a + 6 = (a + 2)(a + 3) a² + 4a + 4 = 0 D = 4² - 4*4*1 = 16 - 16 = 0 a = -4 / 2*1 = -2 a² + 4a + 4 = (a + 2)(a + 2) [latex] \frac{ a^{2} + 5a + 6}{a^{2} + 4a + 4} = \frac{ (a+2)(a+3)}{(a+2)(a+2)} = \frac{a+3}{a+2} [/latex] Ответ: a+3 / a+2 2) [latex] \frac{ x^{2} + 3x + 2}{x^{2} + 6x + 5} [/latex] x² + 3x + 2 = 0 D = 9 - 8 = 1 x₁ = (-3+1) / 2 = -2 / 2 = -1 x₂ = -4 / 2 = -2 x² + 3x + 2 = (x + 1)(x + 2) x² + 6x + 5 = 0 D = 36 - 20 = 16 x₁ = (-6 + 4) / 2 = -2 / 2 = -1 x₂ = -10 / 2 = -5 x² + 6x + 5 = (x + 1)(x + 5) [latex] \frac{ x^{2} + 3x + 2}{x^{2} + 6x + 5} = \frac{(x + 1)(x + 2)}{(x + 1)(x + 5)} = \frac{x+2}{x+5}[/latex] Ответ: x+2 / x+5 3) [latex] \frac{ m^{2} + 2m + 1}{m^{2} + 8m + 7} [/latex] m² + 2m + 1 = 0 D = 4 - 4 = 0 m = -2/2 = -1 m² + 2m + 1 = (m + 1)(m + 1) m² + 8m + 7 = 0 D = 64 - 28 = 36 m₁ = (-8+6) / 2 = -2 / 2 = -1 m₂ = (-8-6) / 2 = -14 / 2 = -7 [latex] \frac{ m^{2} + 2m + 1 }{ m^{2} + 8m + 7 } = \frac{(m+1)(m+1)}{(m+1)(m+7)} = \frac{m+1}{m+7}[/latex] Ответ: m+1 / m+7