Question

√2+√3/2√3-3√2=2-b√6
please help​

Answer 1

Solution!!

(√2 + √3)/(3√2 - 2√3) = 2 - b√6

Rationalize the denominator.

(√2 + √3)/(3√2 - 2√3) × (3√2 + 2√3)/(3√2 + 2√3) = 2 - b√6

[(√2 + √3)(3√2 + 2√3)]/[(3√2 - 2√3)(3√2 + 2√3)] = 2 - b√6

Use (a - b)(a + b) = a² - b² to simplify the expression.

[(√2 + √3)(3√2 + 2√3)]/[(3√2)² - (2√3)²] = 2 - b√6

[(√2 + √3)(3√2 + 2√3)]/[9(2) - 4(3)] = 2 - b√6

[(√2 + √3)(3√2 + 2√3)]/[18 - 12] = 2 - b√6

[(√2 + √3)(3√2 + 2√3)]/[6] = 2 - b√6

Multiply the parentheses.

[6 + 2√6 + 3√6 + 6]/[6] = 2 - b√6

(12 + 5√6)/6 = 2 - b√6

Move the expression with the variable to the left-hand side and change its sign.

(12 + 5√6)/6 + b√6 = 2

Move the constant to the right-hand side and change its sign.

b√6 = 2 - (12 + 5√6)/6

Take the LCM.

b√6 = (12 - (12 + 5√6))/6

b√6 = (12 - 12 - 5√6)/6

b√6 = (-5√6)/6

b = (-5√6)/6 × √6

b = (-5)/6

b = -5/6