SOLUTION: (x+3) / (x-3) > 0 I have the solution, but don't understand how to get there. I understand that multiplying both sides by (x-3) means that x+3

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Question 155569This question is from textbook Algebra 2 with Trigonometry
: (x+3) / (x-3) > 0
I have the solution, but don't understand how to get there. I understand that multiplying both sides by (x-3) means that x+3 > 0. I do not understand how x-3>0 as well. This question is from textbook Algebra 2 with Trigonometry

Found 2 solutions by checkley77, stanbon:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
(x+3)/(x-3)>0 MULTIPLY BOTH SIDES BY (X-3).
(X+3)>(X-3) SUBTRACT X FROM BOTH SIDES.
3>-3 ANSWER.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(x+3) / (x-3) > 0
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Solve the EQUALITY:
(x+3)/(x-3) = 0
True with the numerator is zero
x+3 = 0
x = -3
So, x cannot be -3
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Also, x cannot be 3 for that would make the denominator zero.
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So, draw a number line and mark x =-3 and x = 3 on it.
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That breaks the number line into three intervals.
Test a check value in each interval to see where the solutions
of the INEQUALITY might be.
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(x+3)/(x-3)>0
Let x= -4; you get (-4+3)/(-4-3)>0; true; so solutions in (-inf,-3)
Let x = 0, you get(0+3)/(0-3) >0; false so no solution in (-3,3)
Let x = 4, you get (4+3)/(4-3)>0; true; so solutions in (3,+inf)
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Final solution: x < -3 or x > 3
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Cheers,
Stan H.

SOLUTION: (x+3) / (x-3) > 0 I have the solution, but don't understand how to get there. I understand that multiplying both sides by (x-3) means that x+3 > 0. I do not understand how x-3