Question

Simplify 1-√7/1+√7
by rationalising the denominator.​

Answer 1

$\color{red}{\huge{\underline{\underline{GIVEN\dag}}}}$

• $\frac{1 - \sqrt{7} }{1 + \sqrt{7} }$

$\color{red}{\huge{\underline{\underline{SOLUTION\dag}}}}$

RATIONALISING the DENOMINATOR;

$\frac{1 - \sqrt{7} }{1 + \sqrt{7} } \times \frac{ {1 - \sqrt{7} } }{ {1 - \sqrt{7} } }$

$⇒ \frac{ ({1 - \sqrt{7} })^{2} }{(1 + \sqrt{7})(1 - \sqrt{7} ) }$

$⇒ \frac{ {(1 - \sqrt{7} )}^{2} }{ {(1)}^{2} - ({ \sqrt{7}) }^{2} }$

$⇒ \frac{1 + 7 - 2 \sqrt{7} }{1 - 7}$

$⇒ \frac{8 - 2 \sqrt{7} }{ - 6}$

$⇒ \frac{2(4 - \sqrt{7} )}{ - 6}$

$⇒ \frac{4 - \sqrt{7} }{ - 3}$

$⇒ \color{orange}{{\boxed{\frac{ \sqrt{7} - 4}{3} }}}$

HOPE THAT HELPS!!