How do you divide this logarithmic equation in a TI-83 calculator

I'm supposed to divide this logarithmic equation on a calculator to get an approximate number:

ln 5 / 3 ln 5 + ln 6

My text tells me the answer to this (when calculated and rounded to 3 decimal places is): 0.243

But I just don't understand how they got that number? When I divided the entire equation on the calculator, this was my ending result: 2.655189601

This is exactly how I imputed the equation into the calculator:
ln(5)/3ln(5)+ln(6).

I also tried another method that only seems to work for a more simpler logarithmic equation, but for some reason not for this one:

1) I first imputed ln(5) [or ln(5 - they both have the same results] and got this: 1.609437912
2) Hit the [division] sign
3) Then typed in 3ln(5)+ln(6)
4) and got a completely different answer from the one above: 3.216213739

Is there something I'm doing wrong here? My text doesn't explain to me at all how to compute this equation into my calculator. Can somebody please guide me through a step-by-step process on how to solve this? Thank you, you would be of so much help!

your problem is that you are reading the equation wrong

its (ln5) / [3*ln5+ln6]

enter into calculator just like this:

ln(5)/(3*ln(5)+ln(6))



the answer is .243