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

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

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)   (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)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Multiply EVERY term by the LCD to clear out the fractions.

Simplify

Rearrange the terms.

FOIL

Distribute

Get every term to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

I'll let you check these solutions.
Answer by mananth(16946)   (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

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