Question

решите "Представьте в виде дроби выражение"

Answer 1

а)

$displaystyle frac{x+6}{x+1}^{backslash x-1} - frac{x-6}{x-1}^{backslash x+1} = frac{(x+6)(x-1) - (x-6)(x+1)}{(x+1)(x-1)} =frac{not ! x^2 +5x-not! 6-not ! x^2 +5x +not ! 6}{x^2-1} =\ \ = frac{10x}{x^2-1}$

б)

$displaystyle frac{3}{b^2-3b} + frac{1}{3-b} = frac{3}{b(b-3)} - frac{1}{b-3}^{backslash b} = frac{3-b}{b(b-3)} = -frac{b-3}{b(b-3)} = - frac 1 b$

в)

$displaystyle (2c + 1)^{backslash 2c-1} - frac{5c^2 - 1}{2c - 1} = frac{(2c+1)(2c-1) - 5c^2 + 1}{2c-1} = frac{4c^2 - not !1 - 5c^2 +not !1}{2c-1} = \ \ = -frac {c^2}{2c-1}$

г)

$displaystyle frac{a^2}{a^3 - 9a} - frac{1}{2a - 6} = frac{acdot not ! a}{not ! a(a^2-9)} - frac{1}{2(a-3)} = frac{a}{(a-3)(a+3)}^{backslash 2} - frac{1}{2(a-3)}^{backslash a+3} = \ \ \ = frac{2a - a - 3}{2(a-3)(a+3)} = frac{a-3}{2(a-3)(a+3)} = frac 1 {2(a+3)}$