What is the range of x/((x-1)(x+5)) ?

The range of x/((x-1)(x+5)) is -infinity <f(x)<infinity

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range of x/((x-1)(x+5))

range

\frac{x}{( x - 1 ) ( x + 5 )}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x}{( x - 1 ) ( x + 5 )} = y

Multiply both sides by

(x - 1) (x + 5)

x = y (x - 1) (x + 5)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

x = y (x - 1) (x + 5) : 36 y^{2} - 8 y + 1

36 y^{2} - 8 y + 1 \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

\frac{2}{x ^{2} - 2 x - 3}

f (x) = \frac{7 x + 6}{x - 3}

f (x) = \frac{x - 2}{4 x - 16}

f (x) = \frac{1}{x - 9}

(0.5) (8.1)

What is the range of x/((x-1)(x+5)) ?
The range of x/((x-1)(x+5)) is -infinity <f(x)<infinity