Question

(x-2)/(x+2) + (x+2)/(x-2) = 4​

Answer 1

Answer:

Step-by-step explanation:

$\frac{x-2}{x+2\\}$ + $\frac{x+2}{x-2}$ =4

∴ $\frac{(x-2)^{2} +(x+2)^{2} }{(x+2)(x-2)}$ = 4

$(x+2)^{2}$ + $(x-2)^{2}$ = 4(x-2)(x+2)

∴ ($x^{2}$ +4x+4) + ($x^{2}$-4x+4) = 4($x^{2}$-2x+2x-4)

∴ 2$x^{2}$ + 8 = 4$x^{2}$ - 16

∴ 4$x^{2}$ -2$x^{2}$ =16+8

∴ 2$x^{2}$ = 24

∴ $x^{2}$ = 12

∴ x = √12

∴ x = ±2√3

∴ x = 2√3   OR   x=-2√3