Упростите выражение (x-15)/(√(x+1)-4)-(x-3)/(2+√(x+1)).

\[\frac{x - 15}{\sqrt{x + 1} - 4} - \frac{x - 3}{2 + \sqrt{x + 1}}\]

\[y = \sqrt{x + 1};\ \ y^{2} = x + 1;\ \ \ x = y^{2} - 1\]

\[\frac{y^{2} - 1 - 15}{y - 4} - \frac{y^{2} - 1 - 3}{2 + y} =\]

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

\[= \frac{(y - 4)(y + 4)}{y - 4} - \frac{(y - 2)(y + 2)}{y + 2} =\]

\[= y + 4 - y + 2 = 6.\]