putting everything over a common denominator of (x-2)(x+2), we have
x^2 = 5(x-2)
x^2 - 5x + 10 = 0
then just solve that for x
Make sure that x ≠ ±2 since those values are not allowed in the original equation
x/(x-2) + (2x)/[4-(x^2)] = 5/(x+2)
This calls for finding the common denominator, and then solving for x using the numerators.
Do not forget to exclude the asymptotes values of x where the denominator becomes zero.
LCM (lowest ommon multiple) of denominators (x-2), (4-x²) and (x+2) is (x²-4), since (x-2)(x+2)=(4-x²)
Provided that x≠2 and x≠-2, then we can write the equation above as:
[x(x+2)-2x]/(x²-4) = 5(x-2)/(x²-4)
provided x≠2 and x≠-2
However, the solution does not have real roots. The complex roots are:
If you do not expect complex roots, please check for typos in the original question.
Thank you guys! That is what I got. I wasn't expecting the complex roots.. That's why I wanted to check whether or not I was doing it right!
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