Question

produsul raportului x supra x la 2-10x+25 si x la 2-25 supra x la 2

Answer 1

$\frac{x}{ {x}^{2} - 10x + 25 } \times \frac{ {x}^{2} - 25}{ {x}^{2} }$

$= \frac{x}{ {x}^{2} - 5x - 5x + 25} \times \frac{(x - 5)(x + 5)}{ {x}^{2} }$

$= \frac{x}{x(x - 5) - 5(x - 5)} \times \frac{(x - 5)(x + 5)}{ {x}^{2} }$

$= \frac{x}{(x - 5)(x - 5)} \times \frac{(x -5 )(x + 5)}{ {x}^{2} }$

$= \frac{1}{x - 5} \times \frac{x + 5}{x} = \frac{x + 5}{x(x - 5)} = \frac{x + 5}{ {x}^{2} - 5x}$