What is the limit of 2x + SiNx / x-sinx when x tends to positive infinity?

What is the limit of 2x + SiNx / x-sinx when x tends to positive infinity?

x→+∞
lim (2x+sinx)/(x-sinx)
Divide by X
=lim (2x+sinx)/x / (x-sinx)/x
=lim (2+sinx/x) / (1-sinx/x)
because
SiNx is bounded; 1 / X is infinitesimal
lim(x→+∞) sinx/x=0
Therefore,
simple form
=lim (2+0)/(1-0)
=2
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