What is x+1/(x-2)+2/((x+6)(x-2))-2>= x-3/(x+6)-2 ?

The solution to x+1/(x-2)+2/((x+6)(x-2))-2>= x-3/(x+6)-2 is -6 2

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x+1/(x-2)+2/((x+6)(x-2))-2>= x-3/(x+6)-2

x + \frac{1}{x - 2} + \frac{2}{( x + 6 ) ( x - 2 )} - 2 \geq x - \frac{3}{x + 6} - 2

- 6 < x \leq - \frac{1}{2} or x > 2

Solution steps

x + \frac{1}{x - 2} + \frac{2}{( x + 6 ) ( x - 2 )} - 2 \geq x - \frac{3}{x + 6} - 2

Rewrite in standard form

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

Factor

\frac{4 x + 2}{( x - 2 ) ( x + 6 )} : \frac{2 ( 2 x + 1 )}{( x - 2 ) ( x + 6 )}

\frac{2 ( 2 x + 1 )}{( x - 2 ) ( x + 6 )} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 2 x + 1 )}{( x - 2 ) ( x + 6 )}}{2} \geq \frac{0}{2}

Simplify

\frac{2 x + 1}{( x - 2 ) ( x + 6 )} \geq 0

Identify the intervals

- 6 < x \leq - \frac{1}{2} or x > 2

(x - 3)^{2} (x + 6) > 0

(9^{\frac{5}{3}})^{\frac{3}{10}}

11 h - (2 h - 1) = 118

x^{2} - 10 x + 25 = 3

\frac{3 x}{2} + \frac{1}{6} = \frac{2 x}{3} - \frac{2}{3}

What is x+1/(x-2)+2/((x+6)(x-2))-2>= x-3/(x+6)-2 ?
The solution to x+1/(x-2)+2/((x+6)(x-2))-2>= x-3/(x+6)-2 is -6<x<=-1/2 \lor x>2