Question

Simplificati raportul:
a) x la 2pinus 5pe x plus radical din 5.
b) 3 plus radical din a pe 3radical din a plus a.
c) radical 2 minus 2 pe radical din 2 minus1
d)2radical din 7 minus 7 pe radical din 7////ajutatima va rog

Answer 1

      
[tex]\displaystyle \\ a)~~~ \frac{x^2-5}{x+ \sqrt{5}} =\frac{(x- \sqrt{5})(x+ \sqrt{5})}{x+ \sqrt{5}}=\boxed{x- \sqrt{5}} \\ \\ b)~~~ \frac{3+ \sqrt{a}}{3\sqrt{a}+a}=\frac{3+ \sqrt{a}}{\sqrt{a}(3+\sqrt{a})}=\boxed{\frac{1}{\sqrt{a}}}=\boxed{\frac{\sqrt{a}}{a}} [/tex]


[tex]\displaystyle \\ c)~~~ \frac{ \sqrt{2}-2 }{\sqrt{2}-1}=\frac{ \sqrt{2}(1-\sqrt{2}) }{\sqrt{2}-1}=-\frac{ \sqrt{2} (\sqrt{2}-1) }{\sqrt{2}-1}=\boxed{-\sqrt{2}} \\ \\ d)~~~ \frac{2 \sqrt{7}-7 }{\sqrt{7}}= \frac{\sqrt{7}(2-\sqrt{7})}{\sqrt{7}}=\boxed{2-\sqrt{7}}[/tex]