\[y = \frac{2x^{2} + x - 3}{x - 1} - \frac{x^{2} - 16}{x - 4} =\]
\[= 2x + 3 - x - 4 = x - 1;\ \ \ \]
\[x \neq 1;\ \ x \neq 4\]
\[2x^{2} + x - 3 = 0\]
\[D = 1 + 24 = 25\]
\[x_{1} = \frac{- 1 + 5}{4} = 1;\ \ \ \]
\[x_{2} = \frac{- 1 - 5}{4} = - \frac{6}{4} = - \frac{3}{2}.\]
\[2x^{2} + x - 3 =\]
\[= 2 \cdot (x - 1)\left( x + \frac{3}{2} \right) =\]
\[= (x - 1)(2x + 3).\]
\[y = x - 1;\ \ x \neq 1;\ \ x \neq 4.\]
\[x\] | \[0\] | \[3\] |
---|---|---|
\[y\] | \[- 1\] | \[2\] |