Solve the equation: $\frac{1}{2 x - 5} + \frac{1}{2 x - 11} = \frac{1}{2 x - 7} + \frac{1}{2 x - 9}$ (Equation)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$\frac{1}{2 x - 5} + \frac{1}{2 x - 11} = \frac{1}{2 x - 7} + \frac{1}{2 x - 9} \Rightarrow \frac{1}{2 x - 5} - \frac{1}{2 x - 9} = \frac{1}{2 x - 7} - \frac{1}{2 x - 11} \Rightarrow \frac{2 x - 9 - (2 x - 5)}{(2 x - 5) (2 x - 9)} = \frac{2 x - 11 - (2 x - 7)}{(2 x - 7) (2 x - 11)} \Rightarrow \frac{2 x - 9 - 2 x + 5}{4 x^{2} - 18 x - 10 x + 45} = \frac{2 x - 11 - 2 x + 7}{4 x^{2} - 22 x - 14 x + 77} \Rightarrow \frac{- 4}{4 x^{2} - 28 x + 45} = \frac{- 4}{4 x^{2} - 36 x + 77} \Rightarrow \frac{1}{4 x^{2} - 28 x + 45} = \frac{1}{4 x^{2} - 36 x + 77} \Rightarrow 4 x^{2} - 28 x + 45 = 4 x^{2} - 36 x + 77 \Rightarrow 4 x^{2} - 28 x - 4 x^{2} + 36 x = 77 - 45 \Rightarrow 8 x = 32 ∴ x = \frac{32}{8} = 4$