Need some clarification on this Geometric Series question-q1.jpg
Hi maths helpers,

I need some help with this one
I understand the question and still didn't get the answer. I looked at the worked solution.
I found this
Need some clarification on this Geometric Series question-q2.jpg

What I want to know is why did the author chose to do:

 \frac{\frac{1}{1-x} }{\frac{1}{1-x^2}} = \frac{5}{4}

Please can someone explain
thank you