SOLUTION: Solve the following equation: (7.5)/(x) - (8)/(x-7.5) +1 = 0. This is how I tried to solve this problem: I multiplied everything to get a common denominator ((x-7.5)* (7.5)/(x)

Algebra ->  Equations -> SOLUTION: Solve the following equation: (7.5)/(x) - (8)/(x-7.5) +1 = 0. This is how I tried to solve this problem: I multiplied everything to get a common denominator ((x-7.5)* (7.5)/(x)      Log On


   

Question 771156: Solve the following equation: (7.5)/(x) - (8)/(x-7.5) +1 = 0.
This is how I tried to solve this problem:
I multiplied everything to get a common denominator ((x-7.5)* (7.5)/(x) - (x)*(8)/(x-7.5) +1*(x-7.5)(x)) and got x^2-7.5x-8x-56.25=0 as my new equation. I used the quadratic formula next and ended up with x equaling 0.1/4 and 72.1/-4. I'm not really sure if I was even on the right track with solving this problem, so I would love to see how one of you solve it.
Thanks!

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Clear away the denominators using multiplication of left side and right side by x%28x-7.5%29:

Result is 7.5%28x-7.5%29-8x%2Bx%28x-7.5%29=0, and then do the multiplications indicated ,
7.5x-%287.5%29%5E2-8x%2Bx%5E2-7.5x=0
You should see a quick 0 simplification,
-%287.5%29%5E2-8x%2Bx%5E2=0
x%5E2-8x-%287.5%29%5E2=0, and the rest should be uncomplicated. Just be sure to check for either solution being nonsense according to the original equation.