I am looking trying to follow a solution and am failing to understand the following simplification.
Can someone please break the working out down into the smallest steps to help me understand. How do they get from $(\frac{7}{4})^{n-1} + (\frac{7}{4})^{n-2}$ to that being equal to $(\frac{7}{4})^{n-2}\{\frac{7}{4} + 1\}$ and what is with the curly braces? The rest of the solution I understand.
any help is appreciated.
Treat the curly brackets as ordinary brackets and factor out $\left(\frac74\right)^{n-2}$:
$\quad\left(\dfrac74\right)^{n-1} + \left(\dfrac74\right)^{n-2} \\= \left(\dfrac74\right)^{n-2}\times \dfrac74 + \left(\dfrac74\right)^{n-2}\times 1 \\=\left(\dfrac74\right)^{n-2}\times \left(\dfrac74+1\right) \\=\left(\dfrac74\right)^{n-2}\times \left(\dfrac{11}4\right)$