Question

Why not when you have s+(sx)=60 divide by x to get s+s=60/x thus giving 2s=60/x
and then s = 60/2x and thus 30 /x

Answer 1

You can't do that, because what you do to one side you have to do to the other, and so, you have to divide the entire left side term by x, so you'd get:

s/x + s = 60/x not s+s=60/x

Answer 2

well
s+sx=60
if you divided both sides by x (same as multiplying by 1/x) you would do
(1/x)(s+sx)=(1/x)60
s/x+sx/x=60/x
s/x=s=60
the division carries over to both terms

undistribute s
s(1+x)=60
divide both sides by 1+x
s=$\frac{60}{1+x}$