Question

1. Виконайте дії......​

Answer 1

1. Виконайте дії:

$1) \frac{3}{m} + \frac{5}{n} = \frac{3n}{mn} + \frac{5m}{mn} = \frac{3n + 5m}{mn}$

$2) \frac{x + 4}{2x - 6} - \frac{x - 1}{x - 3} = \frac{x + 4}{2(x - 3)} - \frac{x - 1}{x - 3} = \frac{x + 4 - 2(x - 1)}{2(x - 3)} = \frac{x + 4 - 2x + 2}{2x + 6} = \frac{ - x + 6}{2x - 6}$

$3)\frac{c {}^{2} }{ {c}^{2} - 16 } - \frac{c}{c + 4} = \frac{ {c}^{2} }{(c - 4) \times (c + 4)} - \frac{c}{c + 4} = \frac{ {c}^{2} - c \times (c - 4)}{(c - 4) \times (c + 4)} = \frac{ {c}^{2} - {c}^{2} + 4c }{ {c}^{2} - 16 } = \frac{4c}{ {c}^{2} - 16}$

$4)3y - \frac{18 {y}^{2} }{6y + 1} = \frac{3y \times (6y + 1) - 18y {}^{2} }{6y + 1} = \frac{18 {y}^{2} + 3y - 18 {y}^{2} }{6y + 1} = \frac{3y}{6y + 1}$

$5) \frac{4}{ {c}^{2} - 36 } - \frac{2}{ {c}^{2} - 6c} = \frac{4}{(c - 6) \times ( c+ 6)} - \frac{2}{c \times (c - 6)} = \frac{4c - 2(c + 6)}{c \times (c + 6) \times (c - 6)} = \frac{4c - 2c - 12}{c \times (c + 6) \times (c - 6)} = \frac{2c - 12}{c \times (c + 12) \times (c - 6)} = \frac{2(c - 6)}{c \times ( c + 6)\times (c - 6)} = \frac{2}{c \times ( + 6)} = \frac{2 }{ {c}^{2} + 6c }$