Solve the equation: $\frac{10}{2 x - 5} + \frac{1}{x + 5} = \frac{18}{3 x - 5}$

Created: 6 months ago | Updated: 1 month ago

Job Solution Shahjalal Islami Bank Ltd Shahjalal Islami Bank Ltd. || Trainee Senior Officer (30-11-2018) || 2018 গণিত

$\frac{10}{2 x - 5} + \frac{1}{x + 5} = \frac{18}{3 x - 5} \Rightarrow \frac{10}{2 x - 5} + \frac{1}{x + 5} = \frac{15 + 3}{3 x - 5} \Rightarrow \frac{10}{2 x - 5} + \frac{1}{x + 5} = \frac{15}{3 x - 5} + \frac{3}{3 x - 5}$

$\Rightarrow \frac{10}{2 x - 5} - \frac{15}{3 x - 5} = \frac{3}{3 x - 5} - \frac{1}{x + 5}$ [পক্ষান্তর করে]

$\Rightarrow \frac{10 (3 x - 5) - 15 (2 x - 5)}{(2 x - 5) (3 x - 5)} = \frac{3 (x + 5) - 1 (3 x - 5)}{(3 x - 5) (x + 5)} \Rightarrow \frac{30 x - 50 - 30 x + 75}{(2 x - 5) (3 x - 5)} = \frac{3 x + 15 - 3 x + 5}{(3 x - 5) (x + 5)} \Rightarrow \frac{25}{(2 x - 5) (3 x - 5)} = \frac{20}{(3 x - 5) (x + 5)}$

$\Rightarrow \frac{5}{2 x - 5} = \frac{4}{x + 5}$ [উভয় পক্ষকে 5 দ্বারা ভাগ করে এবং (3x + 5) দ্বারা গুণ করে ]

$\Rightarrow 4 (2 x - 5) = 5 (x + 5)$ [আড় গুণন করে]

$\Rightarrow 8 x - 20 = 5 x + 25 \Rightarrow 8 x - 5 x = 25 + 20 \Rightarrow 3 x = 45 ∴ x = \frac{45}{3} = 15$

∴ নির্ণেয় সমাধান x = 15 (ans)

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Solve the equation: $\frac{10}{2 x - 5} + \frac{1}{x + 5} = \frac{18}{3 x - 5}$