Factorising Indices

[angelina]

Hi, I'm having trouble factorising this problem. If someone could assist it would be greatly appreciated

6^X - 3^x
2^2x-2^x

 

[pappus]

Hi, I'm having trouble factorising this problem. If someone could assist it would be greatly appreciated

6^X - 3^x
2^2x-2^x

\(\displaystyle \displaystyle{\frac{6^x-3^x}{2^{2x}-2^x} = \frac{3^x \cdot 2^x-3^x}{4^{x}-2^x} = \frac{3^x \cdot 2^x-3^x}{2^x \cdot 2^{x}-2^x}}\)

Now factor out \(\displaystyle 3^x\) or \(\displaystyle 2^x\) respectively and cancel the common factor.