Question

Please solve and explain how. Photo attached

Answer 1

Step-by-step explanation:

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