SOLUTION: The problem is: (x+5)/3 + 4/x = 5/6 My instructions are to use the quadratic formula to solve. I think I am supposed to multiply by the common denominator, but I am not sure.
Question 240581: The problem is: (x+5)/3 + 4/x = 5/6 My instructions are to use the quadratic formula to solve. I think I am supposed to multiply by the common denominator, but I am not sure. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! You are correct. Probably the easiest way to proceed is to multiply both sides of the equation by the Lowest Common Denominator (LCD) of all the denominators. The LCD of 3, x and 6 is 6x so we'll multiply both sides by 6x:
On the left side we use the Distributive Property to multiply:
The denominator of each fraction cancels with some part of 6x leaving:
Simplifying this we get:
Since this is a quadratic equation we will solve it by
1) Get one side equal to zero
Subtracting 5x from each side we get:
2) Either factor or use the quadratic formula. We can factor out a 2:
As a sum of squares, there is no way to factor the 2nd factor any further. The only solutions to this equation then are the x's that make equal to zero. But if we think about it, we'll realize that there are no (Real) numbers that will make equal to zero. This is so because would have to be -12 and there are no Real numbers that you can square and get a negative number like -12.
So your equation has no Real solutions. (If you are supposed to find Complex solutions, just use simplify .)
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