What is (12}{x-1}-\frac{12)/x >= 1 ?

The solution to (12}{x-1}-\frac{12)/x >= 1 is -3<= x<0\lor 1<x<= 4

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(12}{x-1}-\frac{12)/x >= 1

\frac{12}{x - 1} - \frac{12}{x} \geq 1

- 3 \leq x < 0 or 1 < x \leq 4

Interval Notation

[- 3, 0) \cup (1, 4]

Solution steps

\frac{12}{x - 1} - \frac{12}{x} \geq 1

Rewrite in standard form

\frac{- x ^{2} + x + 12}{x ( x - 1 )} \geq 0

Factor

\frac{- x ^{2} + x + 12}{x ( x - 1 )} : \frac{- ( x + 3 ) ( x - 4 )}{x ( x - 1 )}

\frac{- ( x + 3 ) ( x - 4 )}{x ( x - 1 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 3 ) ( x - 4 ) ) ( - 1 )}{x ( x - 1 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 3 ) ( x - 4 )}{x ( x - 1 )} \leq 0

Identify the intervals

- 3 \leq x < 0 or 1 < x \leq 4

- 1 + 4

3 m^{3} n - 12 m^{2} n - 180 mn

75 x + 15 \geq 140

5 a^{2} b + 10 ab

3 (x - 5)^{2} + 6 = 54

What is (12}{x-1}-\frac{12)/x >= 1 ?
The solution to (12}{x-1}-\frac{12)/x >= 1 is -3<= x<0\lor 1<x<= 4