Question

Solve for x:
x + 2/ x-2 + x-4 / x+4 =6
(x not equal to 2; -4 )​

Answer 1

Step-by-step explanation:

take lcm

[(x+2)(x+4)+(x-2) (x-4) ]/(x-2/(x+4)=6

[(x^2+2x+4x+8)+(x^2-2x-4x+8)]/(x^2-2x+4x+8)=6

(x^2+6x+8+x^2-6x+8)/x^2+2x+8=6

(2x^2+16)/x^2+2x+8=6

2(x^2+8)= 6(x^2+2x+8)

x^2+8=3(x^2+2x+8)

3x^2+6x+24-x^2-8=0

2x^2+6x+16=0

2(x^2+3x+8)=0

x^2+3x+8=0

using discriminate method

b^2-4ac= (3)^2-4*1*8= 9-32=-23=23i^2

where i is iota, imaginary number

x= (-3+-√(23i^2) )/2

x= (-3+i√23) /2; (-3-i√23) /2