Question

Solve for x
X+1/x-1 + x-2/x+2=3

Answer 1

your answer
hope it help you

Answer 2

The answer is given below :

Now,

(x + 1)/(x - 1) + (x - 2)/(x + 2) = 3

⇒ [(x + 1)(x + 2) + (x - 2)(x - 1)]/[(x - 1)(x + 2)] = 3

⇒ [(x + 1)(x + 2) + (x - 2)(x - 1)] = 3[(x - 1)(x + 2)]

⇒ (x² + 2x + x + 2) + (x² - x - 2x + 2)
= 3(x² + 2x - x - 2)

⇒ x² + 3x + 2 + x² - 3x + 2 = 3(x² + x - 2)

⇒ 2x² + 4 = 3x² + 3x - 6

⇒ 3x² - 2x² + 3x - 6 - 4 = 0

⇒ x² + 3x - 10 = 0

⇒ x² + (5 - 2)x - 10 = 0

⇒ x² + 5x - 2x - 10 = 0

⇒ x(x + 5) - 2(x + 5) = 0

⇒ (x + 5)(x - 2) = 0

So, either, x + 5 = 0 or, x - 2 = 0

i.e., x = -5, x = 2

Therefore, the required solution be

x = -5 and x = 2.

Thank you for your question.