# Homework Help: Divided by highest term in numerator limit

1. Mar 15, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
evaluate.

2. Relevant equations
lim$\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}$

3. The attempt at a solution
i tried diving by highest term in denominator (4^x), but got me no where.

the solution manual has: (divided by highest term in numerator.)with the answer is zero which i don't know how.

lim$_{x->∞}\displaystyle \frac{(\frac{2}{3})^x - 1}{1 + (\frac{4}{3})^x}$ = 0

2. Mar 15, 2013

### Staff: Mentor

Factor 3x out of the numerator and factor 4x out of the denominator.

3. Mar 15, 2013

### Dick

Why didn't dividing by 4^x get you anywhere?