What is x/(x^2-6)>= 1 ?

The solution to x/(x^2-6)>= 1 is -sqrt(6)<x<=-2\lor sqrt(6)<x<= 3

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x/(x^2-6)>= 1

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

- 6 < x \leq - 2 or 6 < x \leq 3

Interval Notation

(- 6, - 2] \cup (6, 3]

Decimal Notation

- 2.44948 \dots < x \leq - 2 or 2.44948 \dots < x \leq 3

Solution steps

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

Rewrite in standard form

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

Factor

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

\frac{- ( x + 2 ) ( x - 3 )}{( x + 6 ) ( x - 6 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 2 ) ( x - 3 ) ) ( - 1 )}{( x + 6 ) ( x - 6 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 2 ) ( x - 3 )}{( x + 6 ) ( x - 6 )} \leq 0

Identify the intervals

- 6 < x \leq - 2 or 6 < x \leq 3

(\frac{7}{3})^{- 1}

4 x^{2} - 4 x

\frac{1}{1. 1 ^{3}}

4 q^{2} + 8 q - 1 = 4

(3 x + 1) (2 x - 3) = (2 x + 1) (3 x - 1)

What is x/(x^2-6)>= 1 ?
The solution to x/(x^2-6)>= 1 is -sqrt(6)<x<=-2\lor sqrt(6)<x<= 3