Question

Упростить выражение (фото ниже)

Answer 1

здравствуй.


$( \frac{x}{x - y} - \frac{x}{y + x} ) \div \frac{x {}^{2} }{x + y} = \frac{2y}{x {}^{2} - xy} \\ \\ 1) \frac{x}{x - y} - \frac{x}{x + y} = \frac{x(x + y) - x(x - y)}{(x - y)(x + y)} = \frac{x {}^{2} + xy - x {}^{2} + xy }{(x - y)(x + y)} = \frac{2xy}{(x - y)(x + y)} \\ \\ 2) \frac{2xy}{(x - y)(x + y)} \div \frac{x {}^{2} }{x + y} = \frac{2xy \times (x + y)}{(x - y)(x + y) \times x {}^{2} } = \frac{2y}{x(x - y)} = \frac{2y}{x {}^{2} - xy }$

удачи в учебе.

Answer 2

( x/(x-y) - x/(y+x)) ÷ x²/(x+y) =

( x(y+x) - x(x-y)/ (x-y)(y+x))  ÷ x²/(x+y) =

( xy+x²-x²+xy/ (x-y)(y+x))  ÷ x²/(x+y) =

(2xy/ (x-y)(y+x))  ÷ x²/(x+y) =

2xy/ (x-y)(y+x) × (x+y)/x² = 2y/ x(x-y)