Mathematics: Rationalize the denominator and simplify. startfraction 5 minus startroot 3 endroot over 4 plus 2 startroot 3 endroot endfraction

7+b i don’t rlly get it lol...

Rationalize the denominator and simplify. startfraction

Ответ:

missdee6929

06.01.2022

Mathematics

$\frac{13-7\sqrt{3}}{2}$

Step-by-step explanation:

We need to rationalize the denominator of $= \frac{5-\sqrt{3}}{4+2\sqrt{3}}$ . For rationalizing we multiply the equation by $\frac{4-2\sqrt{3}}{4-2\sqrt{3}}$

So, solving

$= \frac{5-\sqrt{3}}{4+2\sqrt{3}}*\frac{4-2\sqrt{3}}{4-2\sqrt{3}} \\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{4+2\sqrt{3}*4-2\sqrt{3}}\\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{(4)^2-(2\sqrt{3})^2}\\= \frac{5(4-2\sqrt{3})-\sqrt{3}(4-2\sqrt{3})}{16-(4*3)}\\=\frac{20-10\sqrt{3}-4\sqrt{3}+2*3}{16-12}\\=\frac{20+6-14\sqrt{3}}{4}\\=\frac{26-14\sqrt{3}}{4}\\= \frac{2(13-7\sqrt{3})}{4}\\=\frac{13-7\sqrt{3}}{2}$

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Rationalize the denominator and simplify. startfraction 5 minus startroot 3 endroot over 4 plus 2 startroot 3 endroot endfraction

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