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limits with some fractions

hi

this time i have a question about this problem

Attachment 27640

what is the correct way to solve this kind of problem?

do i get an undefined expression with oo * 0 ?

or do i first simplify the right-hand expression and then multiply the two sides and check what happens when x approaches oo ? the limit is oo.

or do i first multiply the two sides and i get the limit to be 11.1?

thanks for the clarification.

Re: limits with some fractions

Quote:

Originally Posted by

**ryu1** hi

this time i have a question about this problem

Attachment 27640
what is the correct way to solve this kind of problem?

do i get an undefined expression with oo * 0 ?

or do i first simplify the right-hand expression and then multiply the two sides and check what happens when x approaches oo ? the limit is oo.

or do i first multiply the two sides and i get the limit to be 11.1?

thanks for the clarification.

First simplify the right-hand expression and then multiply the two sides . After that divide both numerator and denominator by $\displaystyle x^2$

Re: limits with some fractions

Quote:

Originally Posted by

**princeps** First simplify the right-hand expression and then multiply the two sides . After that divide both numerator and denominator by $\displaystyle x^2$

but if i simplified the hand hand side im left with

(3x-2)(74x+125)

there isnt a denominator here, did i made a mistake?

Re: limits with some fractions

Where's the denominator? Note that

$\displaystyle \frac{6}{4x+7}+\frac{11}{5x+8} = \frac{74x+125}{(4x+7)(5x+8)} = \frac{74x+125}{20x^2+62x+56}$

Can you compute the limit now?

Re: limits with some fractions

yes then i multiply the numerator by 3x-2 (or just the 74x with the 3x)

I get 222x^2

I divide that by 20x^2

it get me to 11.1 thats the limit?

Re: limits with some fractions

Quote:

Originally Posted by

**ryu1** yes then i multiply the numerator by 3x-2 (or just the 74x with the 3x)

I get 222x^2

I divide that by 20x^2

it get me to 11.1 thats the limit?

That is correct!

Re: limits with some fractions

Alright!

I needed a refresher on the simplification of fractions with variables there :)

Thanks!