SOLUTION: 1.) 3x+12=15/x 2.) 3/x-3=5/x^2-9-2/x+3

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: 1.) 3x+12=15/x 2.) 3/x-3=5/x^2-9-2/x+3      Log On


   

Question 737694: 1.) 3x+12=15/x
2.) 3/x-3=5/x^2-9-2/x+3
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
1.) 3x+12=15/x

Clear the fractions. Multiply left and right sides by x. You now have a quadratic equation, easier to solve. Just a little rearranging is needed first.
3x%5E2%2B12x=15
divide b.s. by 3
x%5E2%2B4x=5
x%5E2%2B4x-5=0 and you can finish this one, but check answers against the original equation in case one answer is "extraneous".

2.) 3/x-3=5/x^2-9-2/x+3

That is likely expressed incorrectly so what you want is not clear. If it IS written correctly, then the lowest or simplest denominator is x^2, and you would multiply the left side and right side by x^2 which would clear the fractions.
%283%2Fx-3%29%2Ax%5E2=%285%2Fx%5E2-9-2%2Fx%2B3%29%2Ax%5E2
3x-3x%5E2=5-9x%5E2-2x%2B3x%5E2
3x-3x%5E2%2B9x%5E2-3x%5E2%2B2x-5=0
3x%5E2%2B3x%2B2x%2B5=0
3x%5E2%2B5x%2B5=0
Which use of quadratic formula will give x=%28-5%2B-+sqrt%2825-4%2A3%2A5%29%29%2F15
and that will simplify into x=-%281%2F3%29-%281%2F15%29i%2Asqrt%2835%29 or x=-%281%2F3%29%2B%281%2F15%29i%2Asqrt%2835%29. Complex solutions.