Question

x+2/x-2+x+3/x-3=2

solve the equation please it's very urgent​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt \:  ⟼ \: \dfrac{x + 2}{x - 2} + \dfrac{x + 3}{x - 3} = 2$

$\tt \:  ⟼\dfrac{(x + 2)(x - 3) + (x + 3)(x - 2)}{(x - 2)(x - 3)} = 2$

$\tt \:  ⟼\dfrac{ {x}^{2} - 3x + 2x - 6 + {x}^{2} - 2x + 3x - 6 }{ {x}^{2} - 2x - 3x + 6} = 2$

$\tt \:  ⟼\dfrac{ {2x}^{2} - 12 }{ {x}^{2} - 5x + 6 } = 2$

$\tt \:  ⟼ {2x}^{2} - 12 = 2 {x}^{2} - 10x + 12$

$\tt \:  ⟼10x = 24$

$\tt \:  ⟼ \: x \: = \: \dfrac{12}{5}$

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Verification

Verification Consider LHS

$\tt \:  ⟼\dfrac{x + 2}{x - 2} + \dfrac{x + 3}{x - 3}$

$\tt \:  on \: substituting \: x \: = \dfrac{12}{5} \:, \: we \: get$

$\tt \:  = \dfrac{\dfrac{12}{5} + 2}{\dfrac{12}{5} - 2 } \: + \: \dfrac{\dfrac{12}{5} + 3}{\dfrac{12}{5} - 3}$

$\tt \:  = \dfrac{22}{2} \: + \: \dfrac{27}{( - 3)}$

$\tt \:  = \: 11 \: - \: 9$

$\tt \:  \: = 2$

$\tt \:  ➦ LHS = RHS$

$\tt \:  ⟼ \: Hence,  \: Verified ✔$

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