Question

Сократите дробь
4) a^2 - a√5 / a^2 - 5
6) 7 + √3c / 49 - 3c

Answer 1

$4) \ \dfrac{a^{2}-a\sqrt{5}}{a^{2}-5 } =\dfrac{a(a-\sqrt{5}) }{a^{2} -(\sqrt{5})^{2}}=\dfrac{a(a-\sqrt{5}) }{(a-\sqrt{5})(a+\sqrt{5})}= =\boxed{\dfrac{a}{a+\sqrt{5} }}\\\\\\6) \ \dfrac{7+\sqrt{3c}}{49-3c}=\dfrac{7+\sqrt{3c}}{7^{2}-(\sqrt{3c})^{2}}=\dfrac{7+\sqrt{3c} }{(7+\sqrt{3c})(7-\sqrt{3c} )} =\boxed{\dfrac{1}{7-\sqrt{3c} }}$