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# (x^2-45)/ (x+5) is less than or equal to x

solve the rational inequality. express the solution using interval notation

First of all this inequality does not exist in x=(-5), because we cannot divide by zero.
(x2 - 45)/(x+5) ≤ x .
1. Let's assume that (x+5) > 0 , we can multiply both sides of inequality and keep the same sign "≤"
x2 - 45 ≤ x(x+5) ----> x2 - 45 ≤ x2 +5x
- x2          -x2
----> -45 ≤ 5x ----> 5x / 5 ≥ -45 / 5 ------> x ≥ -9 and x > -5 ----> x > -5
2. Now let's assume (x+5) < 0 , x < -5 ----> when we will divide by (x+5), we have switch sign of inequality to opposite.
x2 - 45 ≥ x(x+5) -------------------> x ≤ -9 and x < -5 ----> x < -5
The answer: (-∞ , -5) U (-5 , ∞) , all real numbers except (-5)

I read it backwards, duh. Nice job! :)

2/18/2013

Thank you, Michael :-)

2/18/2013

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