Question

GUYZZ...
Solve the question in attachment...​

Answer 1

Answer:

$x = 4$

Step-by-step explanation:

Given :

To find the  value of x if,

$\frac{x - 1}{x - 2} - \frac{x - 2}{x - 3} = \frac{x - 5}{x - 6} - \frac{x - 6}{x - 7}$

Solution :

$\frac{x - 1}{x - 2} - \frac{x - 2}{x - 3} = \frac{x - 5}{x - 6} - \frac{x - 6}{x - 7}$

By re-arraging the terms,

We get,

$\frac{x - 1}{x - 2} - \frac{x - 5}{x - 6} =\frac{x - 2}{x - 3} - \frac{x - 6}{x - 7}$

⇒ $\frac{(x - 1)(x - 6) - (x - 5)(x - 2)}{(x - 2)(x - 6)} =\frac{(x - 2)(x - 7) - (x - 6)(x - 3)}{(x - 3)(x - 7)}$

⇒ $\frac{(x^2 - 7x + 6) -(x^2 - 7x + 10)}{(x - 2)(x - 6)} =\frac{(x^2 - 9x + 14) - (x^2 - 9x + 18)}{(x - 3)(x - 7)}$

⇒ $\frac{-4}{(x - 2)(x - 6)} =\frac{-4}{(x - 3)(x - 7)}$

By multiplying by $\frac{1}{-4}$ on both the sides,

We get,

⇒ $(x - 2)(x - 6) = (x - 3)(x - 7)$

⇒ $x^2 - 8x + 12 = x^2 - 10x + 21$

⇒ $x^2 - 8x - x^2 + 10x = 21 - 12$

⇒ $2x = 8$

⇒ $x = 4$