SOLUTION: 5/2x-3 = 3/x-5 no idea how to work it out

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Question 51226: 5/2x-3 = 3/x-5
no idea how to work it out
Found 2 solutions by rapaljer, mathchemprofessor:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Anytime you have a fraction equal to a fraction, like this:5%2F%282x-3%29+=+3%2F%28x-5%29, remember that

a%2Fb=c%2Fd means that a%2Ad=b%2Ac

5%2F%282x-3%29+=+3%2F%28x-5%29 means that 5%2A%28x-5%29+=3%282x-3%29

Now, 5x-25 =6x - 9

Subtract 5x from each side to get all the x terms on the right side:
5x-5x -25= 6x-5x-9
-25 = x-9

Next, add +9 to each side:
-25+9 = x-9+9
-16=x

Check by substituting back into the original equation:
5%2F%282x-3%29+=+3%2F%28x-5%29
5%2F%28-32-3%29=+3%2F%28-16-5%29
5%2F%28-35%29=3%2F%28-21%29
1%2F%28-7%29=+1%2F%28-7%29 It checks!!

R^2 at SCC

Answer by mathchemprofessor(65) About Me  (Show Source):
You can put this solution on YOUR website!
5/2x-3 = 3/x-5
Multiplying both sides by (2x-3)*(x-5),we get,
(5/2x-3)*(2x-3)(x-5)=(3/x-5)*(2x-3)(x-5)
On simplication,we have
5(x-5)=3(2x-3)
5x-25=6x-9
5x-6x=-9+25
-x=16
Multiplying both sides by -1,it becomes
x=-16