Math
posted by April on .
Solve for x.
x/(x2) + (2x)/[4(x^2)] = 5/(x+2)
Please show work!

putting everything over a common denominator of (x2)(x+2), we have
x^2 = 5(x2)
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/(x2) + (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 (x2), (4x²) and (x+2) is (x²4), since (x2)(x+2)=(4x²)
Provided that x≠2 and x≠2, then we can write the equation above as:
[x(x+2)2x]/(x²4) = 5(x2)/(x²4)
provided x≠2 and x≠2
Equating numerators,
x²+2x2x=5(x2)
=>
x²5x+10=0
However, the solution does not have real roots. The complex roots are:
x=(5±√*i)/2 
x=(5±(√15)*i)/2
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!

You're welcome!