# Math Help - algebra 2 please help me!

1. ## algebra 2 please help me!

2x / x^2 - 4

+

1 / x-2

=

2/ x+2

Please solve and state if any solutions are extraneous! Thank you so much!

2. 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.

3. 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!
$\frac{2x}{x^2-4}+\frac{1}{x-2}=\frac{2}{x+2}$

$x^2-4=(x-2)(x+2)$

$LCD=(x+2)(x-2)$

Multiply every term by the LCD and cancel where appropriate.

$2x+x+2=2x-4$

$x+2=-4$

$x=-6$