Question

(x - 2)/(x + 2) - (x + 2)/(x - 2)​

Answer 1

`-\cfrac{8x}{x^2-4}`

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Simplify in below steps:

`\cfrac{x-2}{x+2} -\cfrac{x+2}{x-2} =` Bring to common denominator

`\cfrac{(x-2)^2}{(x+2)(x-2)} -\cfrac{(x+2)^2}{(x+2)(x-2)}=` Multiply both fractions by x +2 or x - 2

`\cfrac{(x-2)^2-(x+2)^2}{(x+2)(x-2)}=` Make a single fraction

`\cfrac{(x-2+x+2)(x-2-x-2)}{(x+2)(x-2)}=` Factorize the numerator

`\cfrac{2x(-4)}{(x+2)(x-2)}=` Simplify the numerator

`-\cfrac{8x}{x^2-4}` Answer

Used identity:

• 
  `(a+b)(a-b)=a^2-b^2`