What is ((x^2-19x+88))/((x^2-11x+24))<= 0 ?

The solution to ((x^2-19x+88))/((x^2-11x+24))<= 0 is 3<x<8\lor 8<x<= 11

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((x^2-19x+88))/((x^2-11x+24))<= 0

\frac{( x ^{2} - 19 x + 88 )}{( x ^{2} - 11 x + 24 )} \leq 0

3 < x < 8 or 8 < x \leq 11

Interval Notation

(3, 8) \cup (8, 11]

Solution steps

\frac{x ^{2} - 19 x + 88}{x ^{2} - 11 x + 24} \leq 0

Factor

\frac{x ^{2} - 19 x + 88}{x ^{2} - 11 x + 24} : \frac{( x - 8 ) ( x - 11 )}{( x - 3 ) ( x - 8 )}

\frac{( x - 8 ) ( x - 11 )}{( x - 3 ) ( x - 8 )} \leq 0

Identify the intervals

3 < x < 8 or 8 < x \leq 11

\frac{2}{m - 1} \geq 1

x^{2} + 4 x < 77

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

- x^{2} + 2 x - 2 < 0

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

What is ((x^2-19x+88))/((x^2-11x+24))<= 0 ?
The solution to ((x^2-19x+88))/((x^2-11x+24))<= 0 is 3<x<8\lor 8<x<= 11