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

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Trying to solve this equation: (X+2)(12/x -1)=12 Have tried many options without success. Thanks      Log On


   

Question 118777: Trying to solve this equation:
(X+2)(12/x -1)=12
Have tried many options without success.
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%2B2%29%2812%2Fx+-1%29=12 Start with the given equation


12x%2Fx-x%2B24%2Fx-2=12 Foil




12-x%2B24%2Fx-2=12 Simplify



x%2812-x%2B24%2Fx-2%29=x%2812%29 Multiply both sides by the LCD x to eliminate every fraction.


12x-x%5E2%2B24-2x=12x Distribute and multiply


12x-x%5E2%2B24-2x-12x=0 Subtract 12x from both sides



-x%5E2-2x%2B24=0 Combine like terms


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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve -x%5E2-2%2Ax%2B24=0 ( notice a=-1, b=-2, and c=24)




x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A-1%2A24+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-2, and c=24



x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A-1%2A24+%29%29%2F%282%2A-1%29 Negate -2 to get 2



x+=+%282+%2B-+sqrt%28+4-4%2A-1%2A24+%29%29%2F%282%2A-1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)



x+=+%282+%2B-+sqrt%28+4%2B96+%29%29%2F%282%2A-1%29 Multiply -4%2A24%2A-1 to get 96



x+=+%282+%2B-+sqrt%28+100+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



x+=+%282+%2B-+10%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%282+%2B-+10%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

x+=+%282+%2B+10%29%2F-2 or x+=+%282+-+10%29%2F-2

Lets look at the first part:

x=%282+%2B+10%29%2F-2

x=12%2F-2 Add the terms in the numerator
x=-6 Divide

So one answer is
x=-6



Now lets look at the second part:

x=%282+-+10%29%2F-2

x=-8%2F-2 Subtract the terms in the numerator
x=4 Divide

So another answer is
x=4

So our solutions are:
x=-6 or x=4