Постройте график функции: y=(5x^2+4x-1)/(x+1)-(x^2-4)/(x-2).

Ответ:

\[y = \frac{5x^{2} + 4x - 1}{x + 1} - \frac{x^{2} - 4}{x - 2} =\]

\[= 5x - 1 - x - 2 = 4x - 3;\ \ \]

\[x \neq - 1;\ \ x \neq 2.\]

\[5x^{2} + 4x - 1 = 0\]

\[D_{1} = 4 + 5 = 9\]

\[x_{1} = \frac{- 2 + 3}{5} = \frac{1}{5};\ \ \ \]

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

\[5x^{2} + 4x - 1 =\]

\[= 5 \cdot (x + 1)\left( x - \frac{1}{5} \right) =\]

\[= (x + 1)(5x - 1).\]

\[y = 4x - 3;\ \ x \neq - 1;\ \ x \neq 2.\]