Упростите выражение: (3/(x+4)+6x/(x^2+x-12)-1/(x-3)):((8x-13)/(x^2-16)).

Ответ:

\[\frac{3^{\backslash x - 3}\ }{x + 4} + \frac{6x}{(x + 4)(x - 3)} - \frac{1^{\backslash x + 4}}{x - 3} =\]

\[= \frac{3x - 9 + 6x - x - 4}{(x + 4)(x - 3)} =\]

\[= \frac{8x - 13}{(x + 4)(x - 3)}\]

\[x^{2} + x - 12 = (x + 4)(x - 3)\]

\[x_{1} + x_{2} = - 1;\ \ x_{1} \cdot x_{2} = - 12\]

\[x_{1} = - 4;\ \ \ x_{2} = 3.\]

\[\frac{8x - 13}{(x + 4)(x - 3)}\ :\frac{8x - 13}{x^{2} - 16} =\]

\[= \frac{(8x - 13)(x - 4)(x + 4)}{(x + 4)(x - 3)(8x - 13)} =\]

\[= \frac{x - 4}{x - 3}.\]