Question

Решить алгебраические дроби

Answer 1

А)$\frac{5}{x^2+5x} + \frac{x+15}{25-x^2} = \frac{5x}{x(5+x)} + \frac{x+15}{(5-x)(5+x)} = \frac{5x(5-x)+x(x+15)}{x(5+x)(5-x)}= \frac{-4x^2+40x}{x(25-x^2)} =$ $\frac{4x(10-x)}{x(25-x^2)} = \frac{4(10-x)}{25-x^2}$
б)$\frac{1}{x+3} + \frac{9x}{x^3+27}= \frac{x^2-3x+9+9x}{(x+3)(x^2-3x+9)} = \frac{(x+3)^2}{(x+3)(x^2-3x+9)} = \frac{x+3}{x^2-3x+9}$