Question

докажи тождество......... ​

Answer 1

Ответ:

Объяснение:

$1.\\ \frac{2x}{x+2} +\frac{4}{x^{2}+5x+6 } -\frac{3}{x+3} = \frac{2x}{x+2}+\frac{4}{x^{2}+2x+3x+6 } -\frac{3}{x+3} =\\= \frac{2x}{x+2}+\frac{4}{x*(x+2)+3*(x+2) } -\frac{3}{x+3} = \frac{2x}{x+2}+\frac{4}{(x+2)*(x+3) } -\frac{3}{x+3} =\\=\frac{2x*(x+3)+4-3*(x+2)}{(x+2)*(x+3)}=\frac{2x^{2}+6x+4-3x-6 }{{(x+2)*(x+3)}} =\frac{2x^{2}+3x-2 }{(x+2)*(x+3)}=\\=\frac{2x^{2}+4x-x-2 }{(x+2)*(x+3)}==\frac{2x*(x+2)-(x+2) }{(x+2)*(x+3)}==\frac{(x+2)*(2x-1) }{(x+2)*(x+3)}=\frac{2x-1}{x+3}.$

$2.\\\frac{\frac{2x-1}{x+3} }{\frac{2x-1}{3} } =\frac{3}{x+3.}$

$3.\\\frac{3}{x+3} +\frac{x}{x+3}=\frac{x+3}{x+3}=1.$