What is 3/(x-1)-4/x >= 1 ?

The solution to 3/(x-1)-4/x >= 1 is -2<= x<0\lor 1<x<= 2

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3/(x-1)-4/x >= 1

\frac{3}{x - 1} - \frac{4}{x} \geq 1

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

Interval Notation

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

Solution steps

\frac{3}{x - 1} - \frac{4}{x} \geq 1

Rewrite in standard form

\frac{- x ^{2} + 4}{x ( x - 1 )} \geq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

6^{2} + 8^{2} = c^{2}

3 x^{3} - 5 x^{2} - 4 x + 4

4 x^{2} - 20 x + 25

x^{2} - 12 x + 27

\frac{m}{2} < 3

What is 3/(x-1)-4/x >= 1 ?
The solution to 3/(x-1)-4/x >= 1 is -2<= x<0\lor 1<x<= 2