Question

answer of this question ​

Answer 1

$\dfrac{x \: + \: \frac{5}{2} }{2x \: - \: \frac{3}{5} }$ - $\dfrac{x \: + \: 3}{2x \: + \: 1}$ = 0

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=> $\dfrac{ \frac{2x \: + \: 5}{2} }{ \frac{10x \: - \: 3}{5} }$ - $\dfrac{x \: + \: 3}{2x \: + \: 1}$ = 0

=> $\dfrac{2x \: + \: 5}{2}$ × $\dfrac{5}{10x \: - \: 3}$ - $\dfrac{x \: + \: 3}{2x \: + \: 1}$ = 0

=> $\dfrac{10x \: + \: 25}{20x \: - \: 6}$ - $\dfrac{x \: + \: 3}{2x \: + \: 1}$ = 0

=> $\dfrac{10x \: + \: 25}{20x \: - \: 6}$ = $\dfrac{x \: + \: 3}{2x \: + \: 1}$

• Cross-multiply them

=> 2x(10x + 25) +1(10x + 25) = 20x(x + 3) -6(x + 3)

=> 20x² + 50x + 10x + 25 = 20x² + 60x - 6x - 18

=> 50x + 10x - 60x + 6x = - 18 - 25

=> 60x - 60x + 6x = - 43

=> 6x = - 43

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x = $\dfrac{-43}{6}$

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