Question

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Answer 1

1)
$4ab + 2 {(a - b)}^{2} = 4ab + 2( {a}^{2} - 2ab + {b}^{2} ) = 4ab + 2 {a}^{2} - 4ab + 2 {b}^{2} = 2 {a}^{2} + 2 {b}^{2}$
2)
$( \frac{3c + 1}{c - 1} + c) \times \frac{1}{c + 1} =\frac{3c + 1 + c(c - 1)}{c - 1} \times \frac{1}{c + 1} = \frac{3c + 1 + {c}^{2} - c}{c - 1} \times \frac{1}{c + 1} = \frac{ {c}^{2} + 2c + 1 }{(c - 1)(c + 1)} = \frac{ {(c + 1)}^{2} }{(c - 1)(c + 1)} = \frac{c + 1}{c - 1}$
3)
$\frac{ {b}^{2} + 4 }{ {b}^{2} - 4 } - \frac{b}{b + 2} = \frac{ {b}^{2} + 4 }{ (b - 2)(b + 2)} - \frac{ b(b - 2)}{(b - 2)(b + 2)} = \frac{ {b}^{2} + 4 - b(b - 2)}{(b - 2)(b + 2)} = \frac{ {b}^{2} + 4 - {b}^{2} + 2b }{(b - 2)(b + 2) } = \frac{2b + 4}{(b - 2)(b + 2)} = \frac{2(b + 2)}{(b - 2)(b + 2)} = \frac{2}{b - 2}$