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

Created: 3 weeks ago | Updated: 6 days ago

Job Solution One Bank Ltd ONE Bank Ltd. || SCO Examination (29-06-2018) || 2018 গণিত

$\frac{x + 3}{x + 2} - \frac{x + 4}{x + 3} = \frac{x + 5}{x + 4} - \frac{x + 6}{x + 5} \Rightarrow \frac{x + 2 + 1}{x + 2} + \frac{1}{x + 2} - \frac{x + 3}{x + 3} - \frac{1}{x + 3} = \frac{x + 4 + 1}{x + 4} + \frac{x + 5 + 1}{x + 5} \Rightarrow \frac{x + 2}{x + 2} + \frac{1}{x + 2} - \frac{x + 3}{x + 3} - \frac{1}{x + 3} = \frac{x + 4}{x + 4} + \frac{1}{x + 4} - \frac{x + 5}{x + 5} - \frac{1}{x + 3} \Rightarrow 1 + \frac{1}{x + 2} - 1 - \frac{1}{x + 3} = 1 + \frac{1}{x + 4} - 1 - \frac{1}{x + 5} \Rightarrow \frac{1}{x + 2} - \frac{1}{x + 3} = \frac{1}{x + 4} - \frac{1}{x + 5} \Rightarrow \frac{x + 3 - (x + 2)}{(x + 2) (x + 3)} = \frac{x + 5 - (x + 4)}{(x + 4) (x + 5)} \Rightarrow \frac{x + 3 - x - 2}{(x + 2) (x + 3)} = \frac{x + 5 - x - 4}{(x + 4) (x + 5)} \Rightarrow \frac{1}{(x + 2) (x + 3)} = \frac{1}{(x + 4) (x + 5)} \Rightarrow (x + 4) (x + 5) = (x + 2) (x + 3) \Rightarrow x^{2} + 5 x + 4 x + 20 = x^{2} + 3 x + 2 x + 6 \Rightarrow x^{2} + 9 x - x^{2} - 5 x = 6 - 20 \Rightarrow 4 x = - 14 ∴ x = \frac{- 14}{4} = \frac{- 7}{2}$

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Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days?

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