Question

No Spam please correct answer​

Answer 1

EXPLANATION.

⇒ x + 3/x - 3 + 6 (x - 3/x + 3) = 5.

As we know that,

⇒ x + 3/x - 3 + 6x - 18/x + 3 = 5.

Taking L.C.M in equation, we get.

⇒ (x + 3)² + (x - 3)(6x - 18)/(x - 3)(x + 3) = 5.

As we know that,

Formula of,

(1) = (x + y)² = x² + y² + 2xy.

(2) = (x² - y²) = (x - y)(x + y).

Using the formula in equation, we get.

⇒ (x² + 9 + 6x) + (6x² - 18x - 18x + 54)/(x² - 9) = 5.

⇒ x² + 9 + 6x + 6x² - 36x + 54 = 5(x² - 9).

⇒ 7x² - 30x + 63 = 5x² - 45.

⇒ 7x² - 5x² - 30x + 63 + 45 = 0.

⇒ 2x² - 30x + 108 = 0.

⇒ x² - 15x + 54 = 0.

Factorizes the equation into middle term split, we get.

⇒ x² - 9x - 6x + 54 = 0.

⇒ x(x - 9) - 6(x - 9) = 0.

⇒ (x - 6)(x - 9) = 0.

⇒ x = 6  and  x = 9.

Answer 2

Answer:

$\dfrac{x + 3}{x - 3} + 6(\dfrac{x - 3}{x + 3}) =\: 5$

Let, $\dfrac{x + 3}{x - 3} = a$

∴ $\dfrac{x - 3}{x + 3} =\: \dfrac{1}{a}$

The equation is, $a + \dfrac{6}{a} = 5$

➻ $\dfrac{{a}^{2} + 6}{a} =\: 5$

➻ a² + 6 = 5a

➻ a² - 5a + 6 = 0

➻ a² - 3a - 2a + 6 =0

➻ a(a - 3) - 2(a- 3) = 0

➻ (a - 3) (a -2) = 0

➻ a - 3 = 0

➻ a = 3

➻ a - 2 = 0

➻ a = 2

➭ If a = 3 then, $\dfrac{x + 3}{x - 3} = 3$

➻ 3x - 9 = x + 3

➻ 3x - x = 3 + 9

➻ 2x = 12

➻ x = $\cancel{\dfrac{12}{2}}$

➻ x = 6

➭ If a = 2 then, $\dfrac{x + 3}{x - 3} = 2$

➻ 2x - 6 = x + 3

➻ 2x - x = 3 + 6

➻ x = 9

∴ Required Solution is x = 6 , 9