Question 982457
By this,  4x+3x^2/4x^2+3x, you may really mean  {{{(4x+3x^2)/(4x^2+3x)}}};

{{{(3x^2+4x)/(4x^2+3x)}}}


{{{(x/x)((3x+4)/(4x+3))}}}, and {{{x/x}}} will not affect this limit;


Degree of leading term in numerator and denominator are equal; leading coefficient take more strength as x approaches or tends toward infinity; so the limit as x approaches infinity is {{{3/4}}}.