SOLUTION: How could I solve this equation dealing with fractions. x/x+4 - 2 = 12/x-12

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Question 277025: How could I solve this equation dealing with fractions.
x/x+4 - 2 = 12/x-12
Found 3 solutions by edjones, jim_thompson5910, mananth:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x/(x+4) - 2 = 12/(x-12)
x(x-12)-2(x+4)(x-12)=12(x+4) multiply each side by (x+4)(x-12) (LCM)
x^2-12x-2(x^2-8x-48)=12x+48
x^2-12x-2x^2+16x+96=12x+48
x^2+8x-48=0 subtract the left side from the right
(x-4)(x+12)=0
x=4, x=-12
.
Ed

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%2B4%29+-+2+=+12%2F%28x-12%29 Start with the given equation


Multiply EVERY term by the LCD %28x%2B4%29%28x-12%29 to clear out the fractions.


%28x-12%29%28x%29-+2%28x%2B4%29%28x-12%29=%28x%2B4%29%2812%29 Simplify


x%28x-12%29-+2%28x%2B4%29%28x-12%29=12%28x%2B4%29 Rearrange the terms.


x%28x-12%29-+2%28x%5E2-8x-48%29=12%28x%2B4%29 FOIL


x%5E2-12x-+2x%5E2%2B16x%2B96=12x%2B48 Distribute


x%5E2-12x-2x%5E2%2B16x%2B96-12x-48=0 Get every term to the left side.


-x%5E2-8x%2B48=0 Combine like terms.


Notice that the quadratic -x%5E2-8x%2B48 is in the form of Ax%5E2%2BBx%2BC where A=-1, B=-8, and C=48


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=-8, and C=48


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64--192+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%2848%29 to get -192


x+=+%288+%2B-+sqrt%28+64%2B192+%29%29%2F%282%28-1%29%29 Rewrite sqrt%2864--192%29 as sqrt%2864%2B192%29


x+=+%288+%2B-+sqrt%28+256+%29%29%2F%282%28-1%29%29 Add 64 to 192 to get 256


x+=+%288+%2B-+sqrt%28+256+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%288+%2B-+16%29%2F%28-2%29 Take the square root of 256 to get 16.


x+=+%288+%2B+16%29%2F%28-2%29 or x+=+%288+-+16%29%2F%28-2%29 Break up the expression.


x+=+%2824%29%2F%28-2%29 or x+=++%28-8%29%2F%28-2%29 Combine like terms.


x+=+-12 or x+=+4 Simplify.


So the solutions are x+=+-12 or x+=+4


I'll let you check these solutions.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
How could I solve this equation dealing with fractions.
x/x+4 - 2 = 12/x-12
x- 2(x+4) / x+4 = 12 / x-12
x-2x-8 / x+4=12/ x-12
(-x-8)(x-12)=(x+4)*12
-x^2+12x-8x+96=12+48
-x^2+4x+96-60=0
-x^2+4x+36=0
x^2-4x-36=0
in the equation a=1, b=-4, c=-36
x1= 4 +sqrt(16+144) /2
=8.325
x2= 4-sqrt(16+144) /2
=-4.325