What is (((x+1)^2*(x-5)^3))/(((x-4)(x+2)))>= 0 ?

The solution to (((x+1)^2*(x-5)^3))/(((x-4)(x+2)))>= 0 is -2 = 5

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(((x+1)^2*(x-5)^3))/(((x-4)(x+2)))>= 0

\frac{( ( x + 1 ) ^{2} \cdot ( x - 5 ) ^{3} )}{( ( x - 4 ) ( x + 2 ) )} \geq 0

- 2 < x < 4 or x \geq 5

Interval Notation

(- 2, 4) \cup [5, \infty)

Solution steps

\frac{( x + 1 ) ^{2} ( x - 5 ) ^{3}}{( x - 4 ) ( x + 2 )} \geq 0

Identify the intervals

- 2 < x < 4 or x \geq 5

(x - 3) (x + 7) > 0

x^{2} + 3 < 0

- 10 x^{4} + 70 x^{3} - 60 x^{2} > 0

\frac{( 3 x + 4 )}{( x - 2 )} < 1

\frac{x + 1}{x} > 3

What is (((x+1)^2*(x-5)^3))/(((x-4)(x+2)))>= 0 ?
The solution to (((x+1)^2*(x-5)^3))/(((x-4)(x+2)))>= 0 is -2<x<4\lor x>= 5