Solve the following mathematical problems with sufficient calculations.

Solve the equation: $\frac{1}{x - 3} + \frac{1}{x - 4} = \frac{1}{x - 2} + \frac{1}{x - 5}$ (Equation)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$\frac{1}{x - 3} + \frac{1}{x - 4} = \frac{1}{x - 2} + \frac{1}{x - 5}$

$\Rightarrow \frac{1}{x - 3} - \frac{1}{x - 5} = \frac{1}{x - 2} - \frac{1}{x - 4}$

$\Rightarrow \frac{x - 5 - x + 3}{(x - 3) (x - 5)} = \frac{x - 4 - x + 2}{(x - 2) (x - 4)}$

$\Rightarrow \frac{- 2}{x^{2} - 5 x - 3 x + 15} = \frac{- 2}{x^{2} - 4 x - 2 x + 8}$

$\Rightarrow \frac{1}{x^{2} - 8 x + 15} = \frac{1}{x^{2} - 6 x + 8}$ [Dividing both sides by - 2]

$\Rightarrow x^{2} - 8 x + 15 = x^{2} - 6 x + 8$

$\Rightarrow - 8 x + 6 x = 8 - 15$

$\Rightarrow - 2 x = - 7$

$∴ x = \frac{- 7}{- 2} = \frac{7}{2} (a n s w e r)$

1 year ago

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