Постройте график функции: y=(2x^2+x-3)/(x-1)-(x^2-16)/(x-4).

Ответ:

\[y = \frac{2x^{2} + x - 3}{x - 1} - \frac{x^{2} - 16}{x - 4} =\]

\[= 2x + 3 - x - 4 = x - 1;\ \ \ \]

\[x \neq 1;\ \ x \neq 4\]

\[2x^{2} + x - 3 = 0\]

\[D = 1 + 24 = 25\]

\[x_{1} = \frac{- 1 + 5}{4} = 1;\ \ \ \]

\[x_{2} = \frac{- 1 - 5}{4} = - \frac{6}{4} = - \frac{3}{2}.\]

\[2x^{2} + x - 3 =\]

\[= 2 \cdot (x - 1)\left( x + \frac{3}{2} \right) =\]

\[= (x - 1)(2x + 3).\]

\[y = x - 1;\ \ x \neq 1;\ \ x \neq 4.\]