Solve the equation : $\frac{4}{2 x + 3} + \frac{15}{5 x + 4} = \frac{35}{7 x + 6}$

Created: 6 months ago | Updated: 2 months ago

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$\frac{4}{2 x + 3} + \frac{15}{5 x + 4} = \frac{35}{7 x + 6} \Rightarrow \frac{4}{2 x + 3} + \frac{15}{5 x + 4} = \frac{21}{7 x + 6} + \frac{14}{7 x + 6} \Rightarrow \frac{4}{2 x + 3} - \frac{14}{7 x + 6} = \frac{21}{7 x + 6} - \frac{15}{5 x + 4} \Rightarrow \frac{28 x + 24 - 28 x - 42}{(7 x + 6) (2 x + 3)} = \frac{105 x + 84 - 105 x - 90}{(5 x + 4) (7 x + 6)} \Rightarrow \frac{- 18}{2 x + 3} = \frac{- 6}{5 x + 4} \Rightarrow \frac{3}{2 x + 3} = \frac{1}{5 x + 4} \Rightarrow 2 x + 3 = 15 x + 12 \Rightarrow 13 x = - 9 ∴ x = \frac{- 9}{13}$ ans.

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