Solve 3^12 - 3^10 / 3^11 + 3^10

[kenewbie]

I'm certain I'm missing something obvious .. again.

I'm having trouble solving the following (using a pen and paper approach)

$$\frac{ 3^{12} - 3^{10} }{ 3^{11} + 3^{10} }$$

I've tried logarithms (I've only covered those with base 10 so far, so any log_n approach is disqualified), messing around with the exponents, roots and factoring, but I can't seem to find a way to do this without actually calculating the individual values.

Enlighten me, please.

k

 

[Dick]

Divide numerator and denominator by 3^10.

 

[HallsofIvy]

Or (same thing really) factor out a 3¹⁰: 3¹¹= 3¹⁰*3 and 3¹²= 3¹⁰*9
$$\frac{3^{12}- 3^{10}}{3^{11}- 3^{10}}= \frac{3^{10}(9- 1)}{3^{10}(3- 1)}$$

 

[kenewbie]

aaah, sweet relief.

thank you.

k