Question on Solving the Expression for the Value of x

Topic : Solve for the value of x

Question : (2 + 2 √3)(2-2x) = (2+√3)(2-√3)- 3√3x

Answer :
2(2) - 2(2x) + 2√3 (2) + 2√3 (-2x) = (2)² - (√3)² - 3√3x
4 - 4x + 4√3 - 4√3 x = 4 - 3 - 3√3x
4 - 4x + 4√3 - 4√3 x = 1 - 3√3x
adding -4 - 4√3 on both sides
4 - 4x + 4√3 - 4√3x - 4 - 4√3 = 1 - 3√3x - 4 - 4√3
-4x - 4√3 x = -3 -4√3 - 3√3x
adding +3√3x on both sides
-4x - 4√3 x + 3√3 x = -3 -4√3 - 3√3x +3√3x
-4x - √3x = -3 - 4√3 (since -4√3 + 3√3 = -√3)
take x as common
x (-4 - √3) = -3 - 4√3
divide both sides by (-4 - √3)
so, x = (-3 - 4√3)/ (-4 - √3)multiply (-4 + √3) to both denominator and numerator on right hand side (rationalization).
x = (-3 - 4√3) x (-4 + √3) / (-4 - √3) x (-4 +√3)
x = [-3(-4) - 3(√3) - 4√3 (-4)- 4√3 (√3)] / [(-4)² - (√3)²]
x = [12 - 3√3 + 16√3 - 12] / [16 - 3]x = 13√3 / 13

x = √3 is the answer.

Hope the Simplification of the Expression will be helpful for you.