Question

le="3 \sqrt{2} - 4 \div \sqrt{3} - 2" alt="3 \sqrt{2} - 4 \div \sqrt{3} - 2" align="absmiddle" class="latex-formula">

Answer 1

Simplify the following:
(3 sqrt(2) - 4)/(sqrt(3) - 2)

Multiply numerator and denominator of (3 sqrt(2) - 4)/(sqrt(3) - 2) by -1:
-(3 sqrt(2) - 4)/(2 - sqrt(3))

-(3 sqrt(2) - 4) = 4 - 3 sqrt(2):
(4 - 3 sqrt(2))/(2 - sqrt(3))

Multiply numerator and denominator of (4 - 3 sqrt(2))/(2 - sqrt(3)) by sqrt(3) + 2:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/((2 - sqrt(3)) (sqrt(3) + 2))

(2 - sqrt(3)) (sqrt(3) + 2) = 2×2 + 2 sqrt(3) - sqrt(3)×2 - sqrt(3) sqrt(3) = 4 + 2 sqrt(3) - 2 sqrt(3) - 3 = 1:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/1

((4 - 3 sqrt(2)) (sqrt(3) + 2))/1 = (4 - 3 sqrt(2)) (sqrt(3) + 2):
Answer: (4 - 3 sqrt(2)) (sqrt(3) + 2)