SOLUTION: Trying to solve this equation: (X+2)(12/x -1)=12 Have tried many options without success. Thanks

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Start with the given equation


Foil




Simplify



Multiply both sides by the LCD x to eliminate every fraction.


Distribute and multiply


Subtract 12x from both sides



Combine like terms


Let's use the quadratic formula to solve for x:


Starting with the general quadratic



the general solution using the quadratic equation is:





So lets solve ( notice , , and )




Plug in a=-1, b=-2, and c=24



Negate -2 to get 2



Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)



Multiply to get



Combine like terms in the radicand (everything under the square root)



Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Lets look at the first part:



Add the terms in the numerator
Divide

So one answer is




Now lets look at the second part:



Subtract the terms in the numerator
Divide

So another answer is


So our solutions are:
or