What is ((x^2-5))/((x-1))>=-1 ?

The solution to ((x^2-5))/((x-1))>=-1 is -3 = 2

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((x^2-5))/((x-1))>=-1

\frac{( x ^{2} - 5 )}{( x - 1 )} \geq - 1

- 3 \leq x < 1 or x \geq 2

Interval Notation

[- 3, 1) \cup [2, \infty)

Solution steps

\frac{x ^{2} - 5}{x - 1} \geq - 1

Rewrite in standard form

\frac{x ^{2} + x - 6}{x - 1} \geq 0

Factor

\frac{x ^{2} + x - 6}{x - 1} : \frac{( x - 2 ) ( x + 3 )}{x - 1}

\frac{( x - 2 ) ( x + 3 )}{x - 1} \geq 0

Identify the intervals

- 3 \leq x < 1 or x \geq 2

x^{4} - 2 x^{2} - 63 \leq 0

\frac{( x - 1 )}{( 2 - x )} \geq 0

\frac{( x + 2 )}{( x ^{2} + 1 )} > \frac{1}{2}

(x^{2} + 1) > 0

\frac{( 5 - 4 x )}{( 3 x ^{2} - x - 4 )} < 4

What is ((x^2-5))/((x-1))>=-1 ?
The solution to ((x^2-5))/((x-1))>=-1 is -3<= x<1\lor x>= 2