Question 446103: 5/2x+3 - 1/x-6 = 0
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! 
1) Factor the denominators. In this case, there is no way to factor further, but if one of them were (for example),  , you would factor it to (x+6)(x-6).
2) Find the least common denominator by multiplying the DIFFERENT factors of the denominators. In this case, it is (2x+3)(x-6).
3) Multiply the LCD found in Step 2 with the entire equation. Note that anything times 0 is 0 and that multiplying with the factor that is the denominator cancels out the denominator (for example,  ). => 5(x-6) - 1(2x+3) = 0
4) Distribute: 5x - 30 - 2x - 3 = 0
5) Add like terms: 3x - 33 = 0
6) Add 33 to both sides: 3x = 33
7) Divide both sides by 3: x = 11
8) Check for excluded values, which are values that make the denominator equal zero, by putting each denominator equal zero and solve for x to find them; the excluded values MUST NOT be included in your answer.
2x+3=0
2x=-3
x-6=0
x=6
Neither of these are x=11, so x=11 is still a valid solution.
9) Therefore, x = {11}
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