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# solve for X

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$${{x+2}\over x^2-2x}-{{2}\over x-2}=-1$$

i need to have X solved...i have no idea...thank you kindly..

Jul 23, 2018

#1
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solve for X
\dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2}=-1

$$\dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2}=-1$$

$$\begin{array}{|rcll|} \hline \dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2} &=& -1 \quad | \quad x-2 \ne 0 \Rightarrow x \ne 2 \\\\ && \quad | \quad x^2-2x \ne 0 \Rightarrow x \ne 2 \\\\ \dfrac{(x+2)(x-2)-2(x^2-2x)}{(x^2-2x)(x-2)} &=& -1 \\\\ (x+2)(x-2)-2(x^2-2x) &=& -(x^2-2x)(x-2) \\ x^2-4-2x^2+4x &=& -(x^2-2x)(x-2) \\ -x^2+4x-4 &=& -(x^2-2x)(x-2) \quad | \quad \cdot (-1) \\ x^2-4x+4 &=& (x^2-2x)(x-2) \\ (x-2)(x-2) &=& (x^2-2x)(x-2) \quad | \quad : (x-2) \\ x-2 &=& x^2-2x \\ x^2-2x &=& x-2 \\ x^2-3x+2 &=& 0 \\ (x-1)(x-2) &=& 0 \\\\ x = 1 && x \ne 2 \\ \hline \end{array}$$ Jul 23, 2018
#3
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Heureka,

thank you very much, although I fail to understand something:

why can't x be equal to 2?

Guest Jul 23, 2018
#3
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Heureka,

thank you very much, although I fail to understand something:

why can't x be equal to 2?

Guest Jul 23, 2018
#7
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If you look closely at the denominator, if x = 2 then you have: x - 2 =2 - 2 =0!!. You should know by now that you cannot divide by zero, because it is "undefined".

Guest Jul 23, 2018
#8
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Heureka,

no worries, I can see why not....thank you very much!!

Guest Jul 23, 2018
#8
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Heureka,

no worries, I can see why not....thank you very much!!

Guest Jul 23, 2018
#10
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why can't x be equal to 2?

Hello Guest,

x can't be equal to 2, because then the denominator is zero.

We must not divide by zero. heureka  Jul 24, 2018
#2
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Solve for x:
(x + 2)/(x^2 - 2 x) - 2/(x - 2) = -1

Bring (x + 2)/(x^2 - 2 x) - 2/(x - 2) together using the common denominator x:
-1/x = -1

Take the reciprocal of both sides:
-x = -1

Multiply both sides by -1:

x = 1

Jul 23, 2018
#5
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thanx guest,