Question

simplify by rationalising the denominator 4✓3-6 4✓3+6​

Answer 1

Answer:

(4√3-6)/(4√3+6) = (21-4√3)/3

Step-by-step explanation:

Given that,

(4√3-6)/(4√3+6)

In both numerator & denominator we can take '2' as common

⇒ 2(2√3-3)/2(2√3+3)

By cancelling,

⇒ (2√3-3)/(2√3+3)

now, to rationalise the denominator

multiply & divide by '(2√3-3)'

⇒ (2√3-3)/(2√3+3) × (2√3-3)/(2√3-3)

⇒ [(2√3-3)(2√3-3)] / [(2√3+3)(2√3-3)]

⇒ (2√3-3)²/((2√3)²-(3)²)

(∵ (a+b)(a-b) = a²-b² & (a-b)² = a²+b²-2ab )

⇒ (2√3)²+(3)²-2(2√3)(3))/(4(3)-9)

⇒ (4(3)+9-4√3)/(12-9)

⇒ (12+9-4√3)/3

⇒ (21-4√3)/3

∴ (4√3-6)/(4√3+6) = (21-4√3)/3

HOPE THIS WOULD BE HELPFUL FOR YOU