What is (((x^2-11x+24)^{101}))/(((x^2-10x+24)^{100))}<= 0 ?

The solution to (((x^2-11x+24)^{101}))/(((x^2-10x+24)^{100))}<= 0 is 3<= x<4\lor 4<x<6\lor 6<x<= 8

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(((x^2-11x+24)^{101}))/(((x^2-10x+24)^{100))}<= 0

\frac{( ( x ^{2} - 11 x + 24 ) ^{101} )}{( ( x ^{2} - 10 x + 24 ) ^{100} )} \leq 0

3 \leq x < 4 or 4 < x < 6 or 6 < x \leq 8

Interval Notation

[3, 4) \cup (4, 6) \cup (6, 8]

Solution steps

\frac{( x ^{2} - 11 x + 24 ) ^{101}}{( x ^{2} - 10 x + 24 ) ^{100}} \leq 0

Factor

\frac{( x ^{2} - 11 x + 24 ) ^{101}}{( x ^{2} - 10 x + 24 ) ^{100}} : \frac{( x - 3 ) ^{101} ( x - 8 ) ^{101}}{( x - 4 ) ^{100} ( x - 6 ) ^{100}}

\frac{( x - 3 ) ^{101} ( x - 8 ) ^{101}}{( x - 4 ) ^{100} ( x - 6 ) ^{100}} \leq 0

Identify the intervals

3 \leq x < 4 or 4 < x < 6 or 6 < x \leq 8

- 3 x^{2} + 8 x + 35 > 0

\frac{4}{( 3 x + 2 )} \geq 0

2 x^{2} - 7 x + 7 > 0

(x + 5) (2 x - 3)^{5} (x - 7)^{3} \cdot (3 x + 8)^{2} < 0

(2 x - 3)^{2} > (2 x + 5) (2 x - 1)

What is (((x^2-11x+24)^{101}))/(((x^2-10x+24)^{100))}<= 0 ?
The solution to (((x^2-11x+24)^{101}))/(((x^2-10x+24)^{100))}<= 0 is 3<= x<4\lor 4<x<6\lor 6<x<= 8