Question

please answer the question​

Answer 1

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Answer 2

Given :–

• $\sf\dfrac{x+3}{x+2}= \dfrac{3x-7}{2x-3}$

To Find :–

• Value of 'x'

Solution :–

$\\\: \: \: \: \: \: \red{ \::\implies \sf \dfrac{x+3}{x+2}= \dfrac{3x-7}{2x-3}}$

$\\\: \: \: \: \: \: \::\implies \sf (x + 3)(2x - 3) = (3x - 7)(x + 2)$

$\\\: \: \: \: \: \: \::\implies \sf 2 {x}^{2} - 3x + 6x - 9=3 {x}^{2} + 6x - 7x - 14$

$\\\: \: \: \: \: \: \::\implies \sf 2 {x}^{2} + 3x- 9=3 {x}^{2} - x- 14$

$\\\: \: \: \: \: \: \::\implies \sf 2 {x}^{2} + 3x- 9 - 3 {x}^{2} + x + 14 = 0$

$\\\: \: \: \: \: \: \::\implies \sf - {x}^{2} + 4x + 5= 0$

$\\\: \: \: \: \: \: \::\implies \sf {x}^{2} - 4x - 5= 0$

$\\\: \: \: \: \: \: \::\implies \sf {x}^{2} - 5x + x - 5= 0$

$\\\: \: \: \: \: \: \::\implies \sf x(x - 5) + 1(x - 5)= 0$

$\\\: \: \: \: \: \: \::\implies \sf (x + 1)(x - 5)= 0$

$\\\: \: \: \: \: \: \::\implies \boxed{ \sf x = 5, - 1}$