What is (x^2-4x-12)/(x^2-6x+8)<= 0 ?

The solution to (x^2-4x-12)/(x^2-6x+8)<= 0 is -2<= x<2\lor 4<x<= 6

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(x^2-4x-12)/(x^2-6x+8)<= 0

\frac{x ^{2} - 4 x - 12}{x ^{2} - 6 x + 8} \leq 0

- 2 \leq x < 2 or 4 < x \leq 6

Interval Notation

[- 2, 2) \cup (4, 6]

Solution steps

\frac{x ^{2} - 4 x - 12}{x ^{2} - 6 x + 8} \leq 0

Factor

\frac{x ^{2} - 4 x - 12}{x ^{2} - 6 x + 8} : \frac{( x + 2 ) ( x - 6 )}{( x - 2 ) ( x - 4 )}

\frac{( x + 2 ) ( x - 6 )}{( x - 2 ) ( x - 4 )} \leq 0

Identify the intervals

- 2 \leq x < 2 or 4 < x \leq 6

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\frac{7 k - 3}{4} = \frac{13 - 5 k}{8}

What is (x^2-4x-12)/(x^2-6x+8)<= 0 ?
The solution to (x^2-4x-12)/(x^2-6x+8)<= 0 is -2<= x<2\lor 4<x<= 6