"Find the limit or explain why it does not exist"

I'm having trouble with these problems, I can't factor/these into a different form.

Having trouble with the algebra.

I've just started calculus and we haven't gone very far so we've just covered limit laws.

I do understand for number 7 that "lim sin(x)/x = 1", but lim sin(2x)/(2x + 3x) doesn't seem right.