Usually, one has to know of a few properties of division by infinity, infinity as an exponent etc. You can easily find a comprehensive list of such properties either online or in any calculus textbook. For your particular cases, "force factorization" will work.
a) limx ->infinity 1/(x+1)=x(1/x)/x(1+1/x)=0 Here I factored both the denominator and the numerator by x; 1/x as x approaches inifnity is 0, so 0/(1+0)=0
b)limx ->inifnity (x^3+x^2-3)/(4x^3)=x^3(1+(1/x)-(3/x^2))/x^3(4)=(1+0-0)/4=1/4