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 Jun 17, 2015

Best Answer 

 #1
avatar+106532 
+13

2 - 12/(4 - x)  = (2x + 4) / (x^2 - 16)   we can rewrite this as

 

2 + 12/(x - 4)   = 2(x + 2)/ [(x - 4) (x + 4) ]        multiply through by [(x - 4) (x + 4) ]

 

2 [(x - 4) (x + 4) ] + 12(x + 4)  = 2(x + 2)        divide thrrough by 2

 

[(x - 4) (x + 4)] + 6(x + 4)  = x + 2    simplify

 

x^2 - 16 + 6x + 24  =  x + 2   

 

x^2 + 6x + 8   = x + 2

 

x^2 + 5x + 6    =  0      factor

 

(x + 3) (x + 2)  = 0      and setting each factor to 0 we have x = -2   or  x = -3 

 

{There are no extraneous solutions }

 

 

 Jun 17, 2015
 #1
avatar+106532 
+13
Best Answer

2 - 12/(4 - x)  = (2x + 4) / (x^2 - 16)   we can rewrite this as

 

2 + 12/(x - 4)   = 2(x + 2)/ [(x - 4) (x + 4) ]        multiply through by [(x - 4) (x + 4) ]

 

2 [(x - 4) (x + 4) ] + 12(x + 4)  = 2(x + 2)        divide thrrough by 2

 

[(x - 4) (x + 4)] + 6(x + 4)  = x + 2    simplify

 

x^2 - 16 + 6x + 24  =  x + 2   

 

x^2 + 6x + 8   = x + 2

 

x^2 + 5x + 6    =  0      factor

 

(x + 3) (x + 2)  = 0      and setting each factor to 0 we have x = -2   or  x = -3 

 

{There are no extraneous solutions }

 

 

CPhill Jun 17, 2015
 #2
avatar+564 
+10

Thank you CPhill!

 Jun 17, 2015

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