SOLUTION: Solve for all values of x: (9/x)+(9/x-2)=12 Solve for x: 125^-2x=25^x+1 Please help me. For the first one I made the bottom equal and started cross multiplying it but then from

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Question 696664: Solve for all values of x: (9/x)+(9/x-2)=12
Solve for x: 125^-2x=25^x+1
Please help me. For the first one I made the bottom equal and started cross multiplying it but then from there got confused cauz I couldn't simplify and my numbers were getting weird. For the second one I don't even know how to do it. We never learned it in class. Thanks in advance!
Answer by Jolliano(16) (Show Source):
You can put this solution on YOUR website!
Multiply through by(x-2)(x). That gives us
9(x-2)(x)/(x) + 9(x-2)(x)/(x-2) = 12(x-2)(x)
Dividing
9(x-2) + 9(x) = 12(x-2)(x)
9x - 18 + 9x = (12x - 24)(x)
18x - 18 = 12x^2 - 24x
COLLECTING LIKE TERMS
-18 = 12x^2 - 24x - 18x
-18 = 12x^2 - 42x
12x^2 - 42x + 18 = 0
DIVIDE THROUGH BY 6
2x^2 - 7x + 3 = 0
2x^2 - 6x - x + 3 = 0
(2x^2 - 6x) + (-x + 3) = 0
2x(x - 3) -1(x - 3) = 0
(2x - 1)(x - 3) = 0
If (2x - 1) = 0
2x = 1
x = 0.5
If (x - 3) = 0
x = 3