Question

1/x-3 + 2/x-2 =8/x through factorization ​

Answer 1

Answer:

$⟹ {5x}^{2} - 40x + 48$

Step-by-step explanation:

$⟹ \frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}$

Taking LCM. :-

$⟹ \frac{1(x - 2) + 2(x - 3)}{(x - 3)(x - 2)} = \frac{8}{x}$

$⟹ \frac{x - 2 + 2x - 6}{ {x}^{2} - 2x - 3x + 6 } = \frac{8}{x}$

$⟹ \frac{3x - 8}{ {x}^{2} - 6x + 6 } = \frac{8}{x}$

BY CROSS MULTIPLICATION :---

$⟹(3x - 8)x = 8( {x}^{2} - 6x + 6)$

$⟹3 {x}^{2} - 8x = 8 {x}^{2} - 48x + 48$

$⟹8 {x}^{2} - 3 {x}^{2} - 48x + 8x + 48 = 0$

$⟹5 {x}^{2} - 40x + 48 = 0.$

I think this is only yoUr answer But if it isn't then solve it more it's a just simply quadratic equation . From here you'll get two values of X .

Now Solve the Quadratic Equation. !!

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Answer 2

$\frac{1}{x-3} +\frac{2}{x-2} =\frac{8}{x}$

→ x(x - 2) + 2x(x - 3) = 8(x - 3)(x - 2)

→ 3x² - 8x = 8x² - 40x + 48

→ -5x² + 32x - 48 = 0

→ 5x² - 32x + 48 = 0

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By factorization :-

→ 5x² - 12x - 20x + 48 = 0

→ x(5x - 12) - 4(5x - 12) = 0

→  (x - 4)(5x - 12) = 0

→ x = 4

or

5x - 12 = 0

5x = 12

x = 12/5