Question

(2m + 2n)^-1 × (2m^-1+2n^1)

Answer 1

Answer:

$( {2m + 2n)}^{ - 1} \times (\frac{1}{2m} + 2n)$

$\frac{1}{2m + 2n} \times \frac{1}{2m} + 2n$

$\frac{1}{2m} ( \frac{1}{2m} + 2n) + \frac{1}{2n} ( \frac{1}{2m} + 2n)$

$\frac{1}{ {4m}^{2} + \frac{n}{m} } + \frac{1}{4mn} + 1$

$\frac{m}{ {4m}^{2} + n } + \frac{1}{4mn} + 1$

$\frac{m}{4 {m}^{2} + n} + \frac{1 + 4mn}{4mn}$

$\frac{m(4mn) + 4 {m}^{2}(1 + 4mn) + n(1 + 4mn) }{4 {m}^{2} (4mn) + n(4mn)}$

$= \frac{4 {m}^{2} n + {4m}^{2} + {4m}^{3}n + n + 4m {n}^{2} }{16 {m}^{3}n + 4m {n}^{2} }$