Divided by highest term in numerator limit

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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
 
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whatlifeforme said:

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 3x out of the numerator and factor 4x out of the denominator.
 
whatlifeforme said:

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?
 

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