Упростите выражение 5/(x-7)-2/x-36x/(x^2-49)+21/(49-x^2).

Ответ:

\[\frac{5}{x - 7} - \frac{2}{x} - \frac{3x}{x^{2} - 49} + \frac{21}{49 - x^{2}} =\]

\[= \frac{5^{\backslash x(x + 7)}}{x - 7} - \frac{2^{\backslash x^{2} - 49}}{x} - \frac{3x^{\backslash x}}{x^{2} - 49} - \frac{21^{\backslash x}}{x^{2} - 49} =\]

\[= \frac{5x(x + 7) - 2 \cdot \left( x^{2} - 49 \right) - 3x \cdot x - 21 \cdot x}{x(x - 7)(x + 7)} =\]

\[= \frac{5x^{2} + 35x - 2x^{2} + 98 - 3x^{2} - 21x}{x(x - 7)(x + 7)} =\]

\[= \frac{14x + 98}{x(x - 7)(x + 7)} =\]

\[= \frac{14 \cdot (x + 7)}{x(x - 7)(x + 7)} = \frac{14}{x(x - 7)}\]

\[\frac{(2p + 1)^{2} - 3p + 2}{p} =\]

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

\[= \frac{4p^{2}}{p} + \frac{p}{p} + \frac{3}{p} = 4p + 1 + \frac{3}{p} \in Z\ \ \]

\[при\ p = - 1;p = 1;p = 3;p = - 3.\]

\[\ \frac{75b^{5}c^{3}}{50b^{4}c^{4}} = \frac{3b}{2c}\]