Question

solve x + 2/x + 3 = 2x - 3/3x - 7
solution set will be {5,-1}

Answer 1

$\huge\sf\underline\red{Answer }$

${\sf{Solution \: set {\implies{5 , -1 }}}}$

Solving and putting the given value

$\sf\implies{ \frac{x + 2}{x + 3} = \frac{2x - 3}{3x - 7} } \: \: \: \: \\ \sf\implies{ \frac{5 + 2}{5 + 3} = \frac{2(5) - 3}{3(5) - 7}} \\ \sf\implies{ \frac{7}{8} = \frac{10 - 3}{15- 7} } \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{ \frac{7}{8} = \frac{7}{8} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\large\sf\underline\pink{Hence \: \: Verified \: ! }$

I hope you understand seeing this answer

and 2nd -1 value you can now able to solve.

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Answer 2

Answer:

$Solution\;set\;=\;\{5,\;-1\}$

Step-by-step explanation:

Given :-

$\frac{x\;+\;2}{x\;+\;3}$ = $\frac{2x\;-3}{3x\;-\;7}$

To find :-

Value of $x$

Solution :-

Cross multiplication :-

$(x\;+\;2)(3x\;-\;7)\;=\;(x\;+\;3)(2x\;-\;3)$

$3x^2\;-\;x\;-\;14\;=2x^2\;+\;3x\;-9$

$x^2\;-\;4x\;-\;5\;=\;0$

$x(x\;-\;5)\;+\;1\1(x\;-\;5)\;=\;0$

$(x\;-\;5)(x\;+\;1)\;=\;0$

$x\;=\;5\;or\;x\;=\;-1$

∴ $Solution\;set\;=\;\{5,\;-1\}$