2x / x^2 - 4 + 1 / x-2 = 2/ x+2 Please solve and state if any solutions are extraneous! Thank you so much!
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Originally Posted by gnarlycarly227 2x / x^2 - 4 + 1 / x-2 = 2/ x+2 Please solve and state if any solutions are extraneous! Thank you so much! 2x(x+2)(x-2) + (x^2 - 4)(x+2) = 2(x-2)(x^2 - 4) 2x(x^2 - 4) + (x+2)(x^2 - 4) - (2x - 4)(x^2 - 4) = 0 (x+6)(x^2 - 4) = 0 x = -6, x = -2 or x = 2 Substitute them back into the original equation. Any answers which don't work are extraneous.
Originally Posted by gnarlycarly227 2x / x^2 - 4 + 1 / x-2 = 2/ x+2 Please solve and state if any solutions are extraneous! Thank you so much! $\displaystyle \frac{2x}{x^2-4}+\frac{1}{x-2}=\frac{2}{x+2}$ $\displaystyle x^2-4=(x-2)(x+2)$ $\displaystyle LCD=(x+2)(x-2)$ Multiply every term by the LCD and cancel where appropriate. $\displaystyle 2x+x+2=2x-4$ $\displaystyle x+2=-4$ $\displaystyle x=-6$
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