Question

Упростите выражение:
$(\frac{2}{x+1} +\frac{10}{x^{2}-3x-4}+\frac{3x}{x-4}):\frac{3x+2}{3}$
15 баллов!!!

Answer 1

Ответ:

Объяснение:

$(\frac{2}{x+1} +\frac{10}{x^{2} -3x-4} +\frac{3x}{x-4} ):\frac{3x+2}{3}=(\frac{2}{x+1} +\frac{10}{x^{2} -4x+x-4} +\frac{3x}{x-4} ):\frac{3x+2}{3}=\\ =(\frac{2}{x+1} +\frac{10}{x*(x-4)+(x-4)} +\frac{3x}{x-4} ):\frac{3x+2}{3}=(\frac{2}{x+1} +\frac{10}{(x-4)*(x+1)} +\frac{3x}{x-4} ):\frac{3x+2}{3}=\\ =\frac{2*(x-4)+10+3x*(x+1)}{(x-4)*(x+1)}:\frac{3x+2}{3}=\frac{2x-8+10+3x^{2} +3x}{(x-4)*(x+1)}:\frac{3x+2}{3} =\frac{3x^{2} +5x+2}{(x-4)*(x+1)}:\frac{3x+2}{3}=$

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