Question

solve the quadratic equation x+1/x-1+x-2/x+2=3(x is not equal to 1,-2

Answer 1

Answer:

Here is your answer----

Step-by-step explanation:

Answer 2

Answer: The values of x are 2 and -5.

Given: $\frac{x+1}{x-1} +\frac{x-2}{x+2} =3$

           x ≠ 1, -2.

To Find: Solution of the quadratic equation.

Solution:

∴ $\frac{(x+1)(x+2)+(x-2)(x-1)}{(x-1)(x+2)} =3$

⇒ $\frac{(x^{2}+2x+x+2) + (x^{2} -x-2x+2) }{x^{2} +2x-x-2} =3$

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

⇒ x² + 3x + 2 + x² - 3x + 2 = 3x² + 3x - 6

⇒ 2x² + 4 = 3x² + 3x - 6

⇒ 3x² - 2x² + 3x - 6 - 4 = 0

⇒ x² + 3x -10 = 0

By the factorising method,

⇒ x² + (5x - 2x) - 10 = 0

⇒ x² + 5x - 2x - 10 = 0

⇒ x (x + 5) - 2 (x + 5) = 0

⇒ (x - 2) (x + 5) = 0

∴ x - 2 = 0                                    ∴ x + 5 = 0

x = 2                                                x = -5

Answer: The values of x are 2 and -5.

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