Question

Выполните сложение дробей:
4a/3a-6 + 3a/8-4a - дробная черта /
3y/4y-4 + 2y/5-5y - дробная черта /
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Answer 1

$\frac{4a}{3a - 6} + \frac{3a}{8 - 4a} = \\ \frac{4a(8 - 4a) + 3a(3a - 6)}{(3a - 6)(8 - 4a)} =$

$\frac{32a - 16 {a}^{2} + {9a}^{2 } - 18a }{(3a - 6)(8 - 4a)} = \frac{14a - 7a {}^{2} }{(3a - 6)(8 - 4a)} =$

$\frac{7a(2 - a)}{3(a - 2) \times 4(2 - a)} = \frac{7a}{12(a - 2)} = \frac{7a}{12a - 24}$

$\frac{3y}{4y - 4} + \frac{2y}{5 - 5y} = \\ \frac{3y(5 - 5y) + 2y(4y - 4)}{(4y - 4)(5 - 5y)} =$

$\frac{15y - {15y}^{2} + {8y}^{2} - 8y}{(4y - 4)(5 - 5y)} = \frac{7y - {7y}^{2} }{4(y - 1)5(1 - y)} =$

$\frac{7y(1 - y)}{4(y - 1)5(1 - y)} = \frac{7y}{20(y - 1)} = \frac{7y}{20y - 20}$