The sum of 4x + y and the opposite of (-8y - 4x + 5)

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natjon528

28.06.2022

Mathematics

Explanation :-At first, we have to multiply the numerator and the denominator and the denominator's inverse such that (a-b)(a+b) = a² - b² is formed in the denominator. Denominator = 5-2√3Rationalizing factor = 5 + 2√3

$\qquad$ _________________________

$\bf Multiplying\:by\:\: \purple{ \dfrac{5+\sqrt{3}}{5+\sqrt{3}}}\\$

$\qquad$ $\longrightarrow \bf \dfrac{1}{5 - 2\sqrt{3} } \times \dfrac{5 + 2\sqrt{3} }{5 + 2\sqrt{3} }\\$

$\qquad$ $\longrightarrow \sf \dfrac{1(5 + 2\sqrt{3}) }{(5 - 2\sqrt{3})(5 + 2\sqrt{3}) }$

$\qquad$ $\longrightarrow \sf \dfrac{5 + 2\sqrt{3} }{ {(5)}^{2} - (2 \sqrt{3})^{2} }$

$\qquad$ $\longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(5 \times 5) - (2 \times 2 \times \sqrt{3} \times \sqrt{3} )}$

$\qquad$ $\longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(25) - (12)}$

$\qquad$ $\purple{ \longrightarrow \bf \dfrac{5 + 2 \sqrt{3} }{13} }$

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