(x^2 + 4x + 4) / (x^2 - 4) = 3
(x+2)^2 / [(x-2)*(x+2) ] = 3
x is not equal to -2 (otherwise we will get 0/0)
thus (x+2)/(x-2)=3
solving, x=4
IMO A
(Algebra) Simple question but I am confused.
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(x² + 4x + 4) = (x + 2)²Rezinka wrote:Q
If (x^2 + 4x + 4) / (x^2 - 4) = 3 ; then x =
A. 4
B. 2
C. 0
D. -2
E. -4
(x² - 4) = (x - 2)(x + 2)
So, (x² + 4x + 4)/(x² - 4) = (x + 2)²/(x - 2)(x + 2) = (x + 2)/(x - 2)
So, (x + 2)/(x - 2) = 3
x = 2 = 3x - 6
8 = 2x
x = 4
The correct answer is A.
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Also try plugging in the ACs. Often the quickest and simplest method.
Can rule out B & D straightaway (as would otherwise be dividing by 0 which is not allowed).
x=0, means the fraction results in -1 (not 3 as needed), so C is out.
Then just plug in 4 or -4 and decide between them. All the numbers are fairly low, so can probably even do the math in your head.
Can rule out B & D straightaway (as would otherwise be dividing by 0 which is not allowed).
x=0, means the fraction results in -1 (not 3 as needed), so C is out.
Then just plug in 4 or -4 and decide between them. All the numbers are fairly low, so can probably even do the math in your head.
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What if you solved this way?Rezinka wrote:Q
If (x^2 + 4x + 4) / (x^2 - 4) = 3 ; then x =
A. 4
B. 2
C. 0
D. -2
E. -4
(x^2 + 4x + 4) / (x^2 - 4) = 3
x^2 +4x+4 = 3x^2 -12
2x^2 -4x-16=0
x^2 -2x-8=0
(x-4) (x+2)=0
x= 4 or x = -2
how can you choose then? I guess because -2 can't be in the denominator so it's out.
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You need not have to stop at this point. In fact you should substitute each value of x into the orignal equation to check its validity.MBA.Aspirant wrote:Rezinka wrote:Q
If (x^2 + 4x + 4) / (x^2 - 4) = 3 ; then x =
A. 4
B. 2
C. 0
D. -2
E. -4
What if you solved this way?
(x^2 + 4x + 4) / (x^2 - 4) = 3
x^2 +4x+4 = 3x^2 -12
2x^2 -4x-16=0
x^2 -2x-8=0
(x-4) (x+2)=0
x= 4 or x = -2
how can you choose then? I guess because -2 can't be in the denominator so it's out.
at x= -2 ,
((-2)^2 + 4x + 4) / ((-2)^2 - 4) = 3 , is undefined as denominator becomes zero. This means x=-2 is not a valid value. Only at x=4 LHS = RHS (left hand side = right hand side)
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