limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x)

解

x \to 4 lim (\frac{2}{x - 4} - \frac{x + 4}{x ^{2} - 4 x})

\frac{1}{4}

十進法表記

0.25

解答ステップ

x \to 4 lim (\frac{2}{x - 4} - \frac{x + 4}{x ^{2} - 4 x})

\frac{2}{x - 4} - \frac{x + 4}{x ^{2} - 4 x} = \frac{2}{x - 4} (1 - \frac{\frac{x + 4}{x ^{2} - 4 x}}{\frac{2}{x - 4}})

= x \to 4 lim (\frac{2}{x - 4} (1 - \frac{\frac{x + 4}{x ^{2} - 4 x}}{\frac{2}{x - 4}}))

簡素化

\frac{2}{x - 4} (1 - \frac{\frac{x + 4}{x ^{2} - 4 x}}{\frac{2}{x - 4}}) : \frac{1}{x}

= x \to 4 lim (\frac{1}{x})

値を挿入する

x = 4

= \frac{1}{4}