Question

For x 1/x+1 +2/x+2= 4/x+4,x is not equal -2,-4 answer is x=2(1+√3),2(1-√3)
I need ste by step explanation

Answer 1

= 1/x+1 + 2/x+2 = 4/x+4

= x +2 + 2(x+1)/(x+1)(x+2) = 4/x+4

= x + 2 + 2x + 2 / x^2 + x + 2x + 2 = 4/x+4

= 3x + 4 / x^2 + 3x + 2 = 4/x+4

= (x+4)(3x+4) = 4(x^2 + 3x + 2 )

= 3x^2 + 12 x + 4x + 16 = 4x^2 + 12x + 8

= x^2 - 4x - 8 = 0

D = b^2 - 4ac

= 16 - 4(-8)(1)

= 16 + 32

= 48

√D = √48

=√2×2×2×2×3

= 4√3

x = -b + √D/2a or -b - √D/2a

= 4 + 4√3 / 2 or 4 - 4√3 / 2

= 2 (1+√3) or 2(1-√3)