Question

6.4.
By using Standard formulae , expand the following

ii (2x + 3/x-1)^2
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Answer 1

Step-by-step explanation:

$= {(2x + \frac{3}{x - 1} )}^{2} \\ = 4 {x}^{2} + \frac{9}{ {(x - 1)}^{2} } + \frac{12x}{x - 1} \\ = \frac{4 {x}^{2} {(x - 1)}^{2} + 9 + 12x(x - 1) }{ {(x - 1)}^{2} } \\ = \frac{4x(x - 1)(x(x - 1) + 3) + 9}{ {x}^{2} + 1 + 2x } \\ = \frac{ (4 {x}^{2} - 4x)( {x}^{2} - x) + 12 {x}^{2} - 12x + 9}{{x}^{2} + 1 + 2x } \\ = \frac{4 {x}^{4} - 4 {x}^{3} - 4 {x}^{3} + 4 {x}^{2} + 12 {x}^{2} - 12x + 9 }{ {x}^{2} + 2x + 1 } \\ = \frac{4 {x}^{4} - 8 {x}^{3} + 16 {x}^{2} - 12x + 9 }{ {x}^{2} + 2x + 1 }$