What is the limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x) ?

The limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x) is 1/4

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

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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}}))

Simplify

\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})

Plug in the value

x = 4

= \frac{1}{4}

\int \frac{x ^{5} - x ^{3} + 4 x}{x ^{4}} d x

\int \frac{sin ( y )}{y} d y

\int 2 x + 7 d x

\int \frac{x ^{3}}{4 + x ^{2}} d x

y = - (2 x - 2)^{\frac{1}{3}}, (- 3, 2)

What is the limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x) ?
The limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x) is 1/4