Divided by highest term in numerator limit

[whatlifeforme]

Homework Statement

evaluate.

Homework Equations

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

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

 

[Mark44]

Homework Statement

evaluate.

Homework Equations

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

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

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

 

[Dick]

Homework Statement

evaluate.

Homework Equations

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

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

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