SOLUTION: I'm not sure if this question has been asked before, but I'm having trouble with two different rational functions. I would really like to learn how to solve them. 1.) 5x / x^2

Question 192976: I'm not sure if this question has been asked before, but I'm having trouble with two different rational functions. I would really like to learn how to solve them.
1.) 5x / x^2 - 25 = 2 / x - 5
2.) 1 + 2 / x = 3 / x^2
Found 2 solutions by RAY100, stanbon:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
please check the problems as we see them
1) (5x)/(x^2-25) = 2/(x-5)
cross multiply
2(x^2-25)=5x(x-5)
factor
2(x+5)(x-5)=5x(x-5)
dividing by (x-5)
2(x+5)=5x
2x+10=5x
10=3x
x=10/3
checking with calc in original matches
2) 1 +2/x=3/(x^2)
multiply by x^2
x^2+2x=3
x^2+2x-3=0
(x+3)(x-1)=0
x=1,(-3)
check by substituting in original matches ok

Answer by stanbon(48564) (Show Source):
You can put this solution on YOUR website!
1.) 5x / (x^2 - 25) = 2 / (x - 5)
lcm = x^2-25 = (x+5)(x-5)
Multiply both sides by the lcm to get:
5x = 2(x+5)
5x = 2x+10
3x = 10
x = 10/3
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2.) 1 + (2 / x) = (3 / x^2)
Multiply thru by x^2 to get:
x^2 + 2x = 3
x^2 + 2x - 3 = 0
(x+3)(x-1) = 0
x = 1 or x = -3
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Cheers,
Stan H.