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how do i solve this? 6/x+4/x+2=1

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1 Answer

Are we supposed to interpret this as:
 
A.  (6/x) + (4/x) +2 = 1
 
or
 
B. (6/x) + [4/(x+2)} = 1?
 
If A., then x = -10
 
If B, then x = -2*[(√7) - 2] or x = 2*[(√7) + 2]

Comments

It is supposed to be interpreted as B. 6 +  4 = 1
                                                      x   x+2
I still don't understand the process of getting to those numbers. I am supposed to
a. solve by completing the square         b. solve using the quadratic formula
OK, so the correct interpretation is B
 
(6/x) + [4/(x+2)} = 1
 
Complete the square method:
 
Multiply by x
 
6 =[4x/(x+2)] = x
 
Multiply by (x + 2)
 
(6)*(x + 2) +4x = (x)*(x + 2) 
 
6x + 12 +4x = x2 +2x
 
6x + 12 + 4x = x2 = 2x
 
Therefore x2 - 8x = 12 or x2 - 8x - 12 = 0  [Let's call this Eq. (1)]
 
Take half the x coefficient, square it, and add to both sides
 
x2 - 8x + 16 = 12 + 16
 
(x - 4)2 + 16 = 28
 
(x - 4)2 = 28
 
from which x = -2*[(√7) - 2] or x = 2*[(√7) + 2]
 
B. Quadratic formula
 
x = [-b ±(b2 - 4ac)1/2]/2a
 
Going back to Eq. (1)
 
a = 1, b = -8, c = -12
 
x = {8 ± [64 - (4)(1)(-12)]1/2}/2(1) = {[8 ± √(112)]}/2}
 
From which
 
x = -2*[(√7) - 2] or x = 2*[(√7) + 2]
 
I hope this helps Mathalina!
 
 
 
 
 
 
 

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