Question

x^2 -4 / x^2 + 3x + 2 × x^2 +x / x^2 - 4x + 4

Answer 1

Răspuns

Explicație pas cu pas:

Answer 2

$\frac{ {x}^{2} - 4 }{ {x}^{2} + 3x + 2 } \times \frac{ {x}^{2} + x }{ {x}^{2} - 4x + 4 } = \frac{ {x}^{2} - {2}^{2} }{ {x}^{2} + x + 2x + 2 } \times \frac{x( \frac{ {x}^{2} }{x} + \frac{x}{x}) }{ {x}^{2} + 2x( - 2) + {( - 2)}^{2} } = \frac{(x - 2)(x + 2)}{x( \frac{ {x}^{2} }{x} + \frac{x}{x}) + 2( \frac{2x}{2} + \frac{2}{2}) } \times \frac{x( {x}^{2 - 1} + 1) }{ {(x - 2)}^{2}} = \frac{(x - 2)(x + 2)}{x( {x}^{2 - 1} + 1) + 2(x + 1) } \times \frac{x(x + 1)}{ {(x - 2)}^{2} } = \frac{(x - 2)(x + 2)}{x(x + 1) + 2(x + 1)} \times \frac{x(x + 1)}{ {(x - 2)}^{2} } = \frac{(x - 2)(x + 2)}{(x + 1)( \frac{x(x + 1)}{x + 1} + \frac{2(x + 1)}{x + 1}) } \times \frac{x(x + 1)}{ {(x - 2)}^{2} } = \frac{(x - 2)(x + 2)}{(x + 1)(x + 2)} \times \frac{x(x + 1)}{ {(x - 2)}^{2} } = \frac{x - 2}{x + 1} \times \frac{x(x + 1)}{ {(x - 2)}^{2} } = \frac{(x - 2)x(x + 1)}{(x + 1) {(x - 2)}^{2} } = \frac{x}{ {(x - 2)}^{2 - 1} } = \frac{x}{x - 2}$