Question

Please solve and explain how. Photo attached

Answer 1

Explanation:

`\frac{4r - 16}{ {r}^(2) } = (1)/(r) + \frac{1}{ {r}^(2) } \\ \\ \therefore \: \frac{4r - 16}{ {r}^(2) } = (1 * r)/(r * r) + \frac{1}{ {r}^(2) } \\ \\ \therefore \: \frac{4r - 16}{ {r}^(2) } = \frac{ r}{ {r}^(2) } + \frac{1}{ {r}^(2) } \\ \\ \therefore \: \frac{4r - 16}{ {r}^(2) } = \frac{ r + 1}{ {r}^(2) } \\ \\ \therefore \: 4r - 16 = \frac{ {r}^(2) (r + 1)}{ {r}^(2) } \\ \\ \therefore \: 4r - 16 =r + 1 \\ \\ \therefore \: 4r - r=1 +16\\ \\ \therefore \: 3r=17\\ \\ \therefore \: r=\ (17)/(3) \\ \\ \huge \red{ \boxed{\therefore \: r= 5\frac{2} {3} }} \ \\`