Question

3. Выполните действия: а) (x+7)/2-(x-13)/2 ( ) б) 4/x+(x-2)/(x+5) ( )
в) 2ху/(х^2-9у^2 )-у/(х-3у)-у/(2х+6у) ( )
решите

Answer 1

$\frac{x + 7}{2} - \frac{x - 13}{2} = \frac{x + 7 - (x + 13)}{2} = \frac{x + 7 - x - 13}{2} = \frac{ - 6}{2} = - 3 \\ \frac{4}{x} + \frac{x - 2}{x + 5} = \frac{4(x + 5) + x(x - 2)}{x(x + 5)} = \frac{4x + 20 + {x}^{2} - 2x }{ {x}^{2} + 5x} = \frac{ {x}^{2} + 2x + 20 }{ {x}^{2} + 5x }$

$\frac{2xy}{ {x}^{2} - 9y {}^{2} } - \frac{y}{x - 3y} - \frac{y}{2x + 6y} = \frac{4xy - 2y(x + 3y) - y(x - 3y)}{2(x + 3y)(x - 3y)} = \frac{4xy - 2xy - 6 {y}^{2} - xy + 3 {y}^{2} }{2(x {}^{2} - 9y {}^{2} ) } = \frac{xy - 3y {}^{2} }{2 {x}^{2} - 18 {y}^{2} }$