Question

упростите выражением​

Answer 1

$\frac{x^{2}+2x+1 }{y^{2}-4 } *\frac{y+2}{x+1}-\frac{x}{y+2} =\frac{(x+1)^{2} }{(y-2)(y+2)} *\frac{y+2}{x+1}-\frac{x}{y+2}=\frac{x+1}{y-2} -\frac{x}{y+2}=\\\\=\frac{xy+2x+y+2-xy+2x}{(y-2)(y+2)} =\frac{4x+y+2}{y^{2}-4 }$

Answer 2

Объяснение:

$\frac{ x^{2} + 2x + 1 }{ {y}^{2} - 4} \cdot \frac{y + 2}{x + 1} - \frac{x}{y + 2} = \\ = \frac{( x + 1)^{ \: \cancel{ 2 \: }} }{ \cancel{({y} + {2})}(y - 2)} \cdot \frac{\cancel{y + 2}}{\cancel{x + 1}} - \frac{x}{y + 2} = \\ = \frac{x + 1}{y - 2} - \frac{x}{y + 2} = \\ = \frac{(x + 1)(y + 2)}{(y + 2)(y - 2)} - \frac{x(y - 2)}{(y + 2)(y - 2)} = \\ = \frac{(x + 1)(y + 2) - x(y - 2)}{(y + 2)(y - 2)} = \\ = \frac{(xy + y + 2x + 2) - (xy - 2x)}{(y + 2)(y - 2)} = \\ = \frac{ \cancel{xy} + y + 2x + 2 - \cancel{xy} + 2x}{(y + 2)(y - 2)} = \\ = \frac{ y + 4x + 2}{(y + 2)(y - 2)}$