What is ((2(x-4)))/(((x-1)(x-7)))<= 1/((x-2)) ?

The solution to ((2(x-4)))/(((x-1)(x-7)))<= 1/((x-2)) is x<1\lor 2<x<7

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((2(x-4)))/(((x-1)(x-7)))<= 1/((x-2))

\frac{( 2 ( x - 4 ) )}{( ( x - 1 ) ( x - 7 ) )} \leq \frac{1}{( x - 2 )}

x < 1 or 2 < x < 7

Interval Notation

(- \infty, 1) \cup (2, 7)

Solution steps

\frac{2 ( x - 4 )}{( x - 1 ) ( x - 7 )} \leq \frac{1}{x - 2}

Rewrite in standard form

\frac{x ^{2} - 4 x + 9}{( x - 1 ) ( x - 7 ) ( x - 2 )} \leq 0

Identify the intervals

x < 1 or 2 < x < 7

(x - 1) (x - 2) \cdot (x - 3)^{2} > 0

\frac{1}{( x + 1 )} > \frac{1}{( x - 2 )}

(x - 1)^{2} (x + 1)^{3} (x - 4) \geq 0

(x + 2) (x + 2) > x (x - 4)

\frac{( x ^{2} - 4 x + 7 )}{( x ^{2} - 7 x + 12 )} < \frac{2}{3}

What is ((2(x-4)))/(((x-1)(x-7)))<= 1/((x-2)) ?
The solution to ((2(x-4)))/(((x-1)(x-7)))<= 1/((x-2)) is x<1\lor 2<x<7