Question

simplify by factorisation method

Answer 1

$\frac{10 + x \sqrt{5} - {x}^{2} }{5 - {x}^{2} } \\ \frac{ {x}^{2} - x \sqrt{5} - 10}{ {x}^{2} - 5 } \\ \frac{ {x}^{2} - 2 \sqrt{5} x + \sqrt{5} x - 10 }{ {x}^{2} - 5 } \\ \frac{x(x - 2 \sqrt{5} ) + \sqrt{5}(x - 2 \sqrt{5} ) }{(x + \sqrt{5} )(x - \sqrt{5}) } \\ \frac{(x + \sqrt{5})(x - 2 \sqrt{5} ) }{(x + \sqrt{5} )(x - \sqrt{5}) } \\ \frac{x - 2 \sqrt{5} }{x - 5}$
please follow me

Answer 2

Numerator =
$- ( {x}^{2} - x \sqrt{5} - 10) \\ = > - ( {x}^{2} - 2 \sqrt{5} x + \sqrt{5x} - 10) \\ = > - (x(x - 2 \sqrt{5} ) + \sqrt{5} (x - 2 \sqrt{5} )) \\ = > - (x + \sqrt{5} )(x - 2 \sqrt{5} )$
denominator =
$= > - ( {x}^{2} - 5) \\ = > - (x + \sqrt{5} )(x - \sqrt{5} )$
Numerator divided by denominator =
$x - 2 \sqrt{5} \div x - \sqrt{5}$
after rationalisation get the answer....

HOPE THIS WOULD HELP YOU