Сократите дробь:
а) $\frac{x^2 - 49}{16 - (x - 3)^2}$;
б) $\frac{81 - 36t + 4t^2}{(2t - 3)^2 - 36}$;
в) $\frac{(x - 1)^2 - 144}{x^2 - 121}$;
г) $\frac{25 - (5x - 1)^2}{36 - 60x + 25x^2}$.
$\frac{x^2 - 49}{16 - (x - 3)^2} = \frac{(x - 7)(x + 7)}{(4 - (x - 3))(4 + x - 3)} = \frac{(x - 7)(x + 7)}{(4 - x + 3)(1 + x)} = \frac{(x - 7)(x + 7)}{(7 - x)(1 + x)} = -\frac{(x - 7)(x + 7)}{(x - 7)(x + 1)} = -\frac{x + 7}{x + 1}$
$\frac{81 - 36t + 4t^2}{(2t - 3)^2 - 36} = \frac{(9 - 2t)^2}{(2t - 3 - 6)(2t - 3 + 6)} = \frac{(2t - 9)^2}{(2t - 9)(2t + 3)} = \frac{2t - 9}{2t + 3}$
$\frac{(x - 1)^2 - 144}{x^2 - 121} = \frac{(x - 1 - 12)(x - 1 + 12)}{(x - 11)(x + 11)} = \frac{(x - 13)(x + 11)}{(x - 11)(x + 11)} = \frac{x - 13}{x - 11}$
$\frac{25 - (5x - 1)^2}{36 - 60x + 25x^2} = \frac{(5 - (5x - 1))(5 + 5x - 1)}{(6 - 5x)^2} = \frac{(5 - 5x + 1)(4 + 5x)}{(6 - 5x)^2} = \frac{(6 - 5x)(4 + 5x)}{(6 - 5x)^2} = \frac{4 + 5x}{6 - 5x}$
Пожауйста, оцените решение
