solve x+5+(4/x)=0

That was good logic JonyMyster.  When there is a squared term there are often 2 answers.  

ok heres how id do it

x+5+(4/x) = 0
subtract 4/x from both sides
x+5=-4/x
multiply both sides by x
(x + 5)x = -4

distribute

x² + 5x = -4
think about it for a moment and realize that the only way to get -4 is for x to be negative, but if its too big the x² will be too big for 5x to bring it down to -4. now to guess at some numbers because its late and im tired

-1² + 5(-1) = -4

1 - 5 = -4

bingo

x = -1

solved like a pro

im sorry im terrible at math

x + 5 + 4/x = 0

Multiply all terms by x

x² + 5x + 4 = 0

This factorises as:

(x + 1)(x + 4) = 0

So the two solutions are:  x = -1  and  x = -4

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