Question

Упростить:
1) $\frac{2}{x-1} + \frac{6}{1-x}$
2) $\frac{2}{x} + \frac{3}{x+1}$
3) $\frac{4}{x^2} + \frac{6}{x^3}$

Answer 1

$1) \frac{2}{x-1} + \frac{6}{1-x} = \frac{2}{x-1} - \frac{6}{x-1} = \frac{2-6}{x-1} =- \frac{4}{x-1}$
$2) \frac{2}{x} + \frac{3}{x+1} = \frac{2(x+1)+3x}{x(x+1)} = \frac{2x+2+3x}{ x^{2} +x}= \frac{5x+2}{ x^{2} +x}$
$3) \frac{4}{ x^{2} } + \frac{6}{ x^{3} } = \frac{4x+6}{ x^{3} }$