SOLUTION: How do I solve for "x" (2x)/(x+4)-1/(x-3)=0

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Question 203380: How do I solve for "x"
(2x)/(x+4)-1/(x-3)=0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0
The best way to start is to eliminate the fractions. You can eliminate the fractions by multiplying both sides of the equation by the Lowest Common Denominator (LCD) of all the fractions (including, if any fractions on both sides).
The LCD of the fractions in this equation is: (x+4)(x-3). Multiplying both side by the LCD:

On the left side we need to use the Distributive Property:

Simplify

%28x-3%29%282x%29+-+%28x%2B4%29%281%29+=+0
2x%5E2+-+6x+-+%28x%2B4%29+=+0
2x%5E2+-6x+-+x+-+4+=+0
2x%5E2+-7x+-4+=+0
This is a quadratic equation. We can solve it by factoring or the Quadratic Formula (or by completing the square). This factors so:
%282x+%2B+1%29%28x+-+4%29+=+0
In order for this product to be zero, one of the factors must be zero (Zero Product Property):
2x+%2B+1+=+0 or x+-+4+=+0
Solving each:
x+=+-1%2F2 or x+=+4
So there are two solutions to: %282x%29%2F%28x%2B4%29+-+1%2F%28x-3%29=0