What is 2+1/(x-3)>= 1/(x-1) ?

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

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

2 + \frac{1}{x - 3} \geq \frac{1}{x - 1}

x < 1 or x = 2 or x > 3

Interval Notation

(- \infty, 1) \cup x = 2 \cup (3, \infty)

Solution steps

2 + \frac{1}{x - 3} \geq \frac{1}{x - 1}

Rewrite in standard form

\frac{2 x ^{2} - 8 x + 8}{( x - 3 ) ( x - 1 )} \geq 0

Factor

\frac{2 x ^{2} - 8 x + 8}{( x - 3 ) ( x - 1 )} : \frac{2 ( x - 2 ) ^{2}}{( x - 3 ) ( x - 1 )}

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < 1 or x = 2 or x > 3

\frac{4 x - 11}{4} \leq 0

\frac{3 + t}{14} - \frac{t + 1}{6} > - \frac{1}{42}

\frac{1}{50} + \frac{1}{75}

9 (a - b)^{2} + 12 (a - b) (a + b) + 4 (a + b)^{2}

- 10 x = 2 x^{2}

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