Question

2/(x-3)+1(x-1)=5/(x-1)-2/(x-2)

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\frac{7}{3}$ is the required value of $\frac{2}{(x -3)} + \frac{1}{(x -1)} = \frac{5}{(x -1)} - \frac{2}{(x -2)}$

Step-by-step explanation:

Explanation:

Given in the question that,

$\frac{2}{(x -3)} + \frac{1}{(x -1)} = \frac{5}{(x -1)} - \frac{2}{(x -2)}$

Step 1:

We have, $\frac{2}{(x -3)} + \frac{1}{(x -1)} = \frac{5}{(x -1)} - \frac{2}{(x -2)}$

⇒ $\frac{2(x -1)+ 1(x -3)}{(x -3)(x -1)} = \frac{5(x -2)-2(x -1)}{(x - 1)(x -2)}$

⇒$\frac{(2x -2+ x -3)}{(x -3)(x -1)} = \frac{(5x -10-2x +2)}{(x - 1)(x -2)}$

⇒  $\frac{(3x -5)}{(x -3)(x -1)} = \frac{(3x -8)}{(x - 1)(x -2)}$

⇒$\frac{(3x -5)}{(x -3)} = \frac{(3x -8)}{(x -2)}$

⇒ (3x -5)(x -2) = (3x -8)(x -3)

⇒($3x^2 - 6x -5x + 10 = 3x^2 - 9x -8x + 24$)

⇒ -6x - 5x + 10 = -9x -8x + 24

⇒-11x + 10 = -17x + 24

⇒-11x +17x = 24 - 10

⇒ 6x = 14

⇒ x = $\frac{14}{6} = \frac{7}{3}$

Final answer:

Hence, $\frac{7}{3}$ is the required value of $\frac{2}{(x -3)} + \frac{1}{(x -1)} = \frac{5}{(x -1)} - \frac{2}{(x -2)}$

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