Solve the following equation. Check all proposed solutions. Show all work in solving and checking, and state your final answer
my work
First let's add the fractions on the left. To add any fraction, you must put them over a common denominator, in this case $(x+2)(x^2-4)$
Multiply out the numerator and denominator then combine like terms, but after doing all that I got
$-16=x^3+4x^2-17x $
and I can't get value for $x$
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You forgot to factorize $(x^2 - 4) = (x + 2)(x -2)$ from the denominator. Then the LCM becomes $(x^2 - 4)$ in which case the numerator gives
$5(x - 2) - 4 = (x-3)(x + 2)$, so you will get $(x^2-6x+8) = 0$ which is $(x- 4)(x-2) = 0$. Looking at the equation $\color{red}{x = 4}$ is the only solution. This is because when you put $x = 2$, the original equation is undefined.
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