What is the limit as x approaches 1-of (3+x)/(x^2-1) ?

The limit as x approaches 1-of (3+x)/(x^2-1) is -infinity

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limit as x approaches 1-of (3+x)/(x^2-1)

x \to 1 - lim (\frac{3 + x}{x ^{2} - 1})

- \infty

Solution steps

x \to 1 - lim (\frac{3 + x}{x ^{2} - 1})

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

= x \to 1 - lim ((3 + x) \frac{1}{x ^{2} - 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 1 - lim (3 + x) \cdot x \to 1 - lim (\frac{1}{x ^{2} - 1})

x \to 1 - lim (3 + x) = 4

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

= 4 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{d}{d x} (- \frac{15}{8 x ^{\frac{7}{2}}})

\int \frac{1}{( x ^{3} + 1 )} d x

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{3 t}

\int \frac{- 2 sec ^{2} ( x )}{( 4 + tan ( x ) ) ^{3}} d x

y = e^{9 e^{x}}

What is the limit as x approaches 1-of (3+x)/(x^2-1) ?
The limit as x approaches 1-of (3+x)/(x^2-1) is -infinity