Question

Simplify each of the following by rationalising
the denominator:
(i)
5+ √6÷
5-16
please help me !​

Answer 1

Given:

5+ √6÷5-√6

Aim : To simplify the given fraction by rationalizing the denominator:

Step-by-step explanation:

                $\frac{5+\sqrt{6} }{5-\sqrt{6} }$

• Multiplying the numerator and denominator by        $\frac{5+\sqrt{6} }{5+\sqrt{6} }$

       now , our fraction become

•                        $\frac{5+\sqrt{6} }{5-\sqrt{6} }$     ×     $\frac{5+\sqrt{6} }{5+\sqrt{6} }$

•                           $\frac{(5+\sqrt{6} )^2}^{5^2-6}$        

                                 

•                            $\frac{25+10\sqrt{6}+6 }{25-6}$

•                            $\frac{31+10\sqrt{6} }{19}$

                                       

                                   Hence $\frac{31+10\sqrt{6} }{19}$  is the simplest form of  $\frac{5+\sqrt{6} }{5-\sqrt{6} }$