Question

Сократив дробь (3x²-xy+12x-4y)/(2x²+xy+8x+4y) вычеслите при y/x=-3

Answer 1

$\frac{3x^2-xy+12x-4y}{2x^2+xy+8x+4y} = \frac{(3x^2+12x)-(xy+4y)}{(2x^2+8x)+(xy+4y)}= \\ \\ = \frac{3x(x+4)-y(x+4)}{2x(x+4)+y(x+4)}= \frac{(x+4)*(3x-y)}{(2x+y)*(x+4)}= \frac{3x-y}{2x+y} \\ \\ \frac{y}{x}=-3 =\ \textgreater \ y=-3x \\ \\ \frac{3x+3x}{2x-3x}= \frac{6x}{-x}=-6$