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

The solution to 6/(x-1)-6/x >= 1 is -2<= x<0\lor 1<x<= 3

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

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

- 2 \leq x < 0 or 1 < x \leq 3

Interval Notation

[- 2, 0) \cup (1, 3]

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 2 \leq x < 0 or 1 < x \leq 3

- 5 x^{2} y + 10 x y - 15 x y^{2}

5^{- 2} \cdot 5^{5}

5 \leq 1 - r

3 n + 75 = 50 + 2 n

4 - 6 v > 19 - 3 v

What is 6/(x-1)-6/x >= 1 ?
The solution to 6/(x-1)-6/x >= 1 is -2<= x<0\lor 1<x<= 3