Question

x-3/x+3-x+3/x-3+6×6/7=0​

Answer 1

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Question :

$\blue\bigstar\rm{\dfrac{x-3}{x+3}-\dfrac{x+3}{x-3}+ 6 \times\dfrac{6}{7}=0}$

To find :

The value of x=?

$\large\sf{\underline{\color{red} \: Solution :}}$

$\\ \implies \sf \: \frac{x - 3}{x + 3} - \frac{x + 3}{x - 3} + 6 \times \frac{6}{7} = 0$

$\\ \implies \sf \: \: \frac{(x - 3)(x - 3) - (x + 3)(x + 3)}{(x + 3)(x - 1)} + 6 \times \frac{6}{7}$

$\\ \implies \sf \: \frac{x(x - 3) - 3(x - 3) - (x(x + 3) + 3(x + 3))}{x(x - 3) + 3(x - 3)} + \frac{36}{7} = 0$

$\\ \implies \sf \: \frac{ {x}^{2} - 3x - 3x + 3 - ( {x}^{2} + 3x + 3x + 9)}{ {x}^{2} - 3x + 3x - 9} + \frac{36}{7} = 0$

$\\ \implies \sf \: \frac{ ({x}^{2} - 6x + 3) - {x}^{2} - 6x - 9}{ {x}^{2} - 9} + \frac{36}{7} = 0$

$\\ \implies \sf \: \frac{ {x}^{2} - 6x + 3 - {x}^{2} - 6x - 9 }{ {x}^{2} - 9 } + \frac{36}{7} = 0$

$\\ \implies \sf \: \frac{ - 12x - 6}{ {x}^{2} - 9 } + \frac{36}{7} = 0$

$\\ \implies \sf \: \frac{ - 12x - 6}{ {x}^{2} - 9} = - \frac{36}{7}$

$\\ \implies \sf \: 7( - 12x - 6) = - 36( {x}^{2} - 9)$

$\\ \implies \sf \: - 84x - 42 = - 36 {x}^{2} + 324$

$\\ \implies \sf \: - 84x - 42 + 36 {x}^{2} - 324 = 0$

$\\ \implies \sf \: 36 {x}^{2} - 84x - 366 = 0$

$\\ \implies \sf \: 18 {x}^{2} - 42x - 183 = 0 \: \: ...from \: dividing \: by \: 2$

$\\ \implies \sf \: 6 {x}^{2} - 14x - 61 = 0 \: \: \: from \: dividing \: by \: 3$

$\\ \implies \sf \: 6 {x}^{2} - 14x - 61 = 0$

$\bullet { \underline{ \bf{by \: using \: determinant \: method}}}$

$\implies \sf \: {b}^{2} - 4ac$

$\\ \implies \sf \: {(14)}^{2} - 4(6)(61)$

$\implies \sf \: 196 - 1464$

$\\ \implies \sf \: - 1268$

$\bullet \underline{ \bf{by \:using \: formula \: method}}$

$\\ \implies \sf \: x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

$\\ \implies \sf \: x = \frac{14 \pm \sqrt{ - 1268} }{2 \times 6}$

$\\ \implies \sf \: x = \frac{14 \pm \: 2 \sqrt{317} }{12}$

$\\ \implies \large \sf \: x = \frac{7 \pm \sqrt{317} }{6}$

$\bullet \bf { roots \: of \: this \: quadratic \: equation \: is \: x = \frac{7 + \sqrt{317} }{6} \: and \: x = \frac{7 - \sqrt{317} }{6} }$

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Answer 2

Answer:

given 3(x - 4) + 5(x + 6) - 8(x - 7) = 0  

3x - 12 + 5x + 30 - 8x + 56 = 0  

8x - 12 + 30 - 8x = 0

+8x - 8x =0

Step-by-step explanation: