Question

How would I solve this rational equation


`(4)/(x) = \frac{1}{ {x }^(2) + 4x} + (5)/(x)`

Answer 1

`(4)/(x)=(1)/(x^2+4x)+(5)/(x), x \\eq 0, x \\eq -4. \\ewline (4)/(x)-(1)/(x^2+4x)-(5)/(x)=0. \\ewline \frac{4}[x}-(1)/(x(x+4))-(5)/(x)=0. \\ewline (4(x+4)-1-5(x+4))/(x(x+4))=0. \\ewline (-x-5)/(x(x+4))=0. \\ewline -x-5=0. \\ewline -x = 5. \\ewline x = -5.`