Question

Hey!
Please solve this question.

solve the equation for x: (x + 3)/(x - 2) - (1 - x)/x = 17/x

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Answer 1

$\huge\boxed{\mathfrak{\fcolorbox{red}{skyblue}{Here \:is\:Ans}}}$

$\frac{x + 3}{x - 2} - \frac{1 - x}{x} = \frac{17}{x}$


$\frac{x + 3}{x - 2} - \frac{1 - x}{x} - \frac{17}{x} = 0$



$\frac{x \times (x + 3) - (x - 2) \times (x - 1) - 17(x - 2)}{x \times (x - 2)} = 0$



$\frac{x {}^{2} + 3x - (x - x {}^{2} - 2 + 2x) - 17 x + 34 }{x \times (x - 2)} = 0$


❄Collect The Like Terms



$\frac{x {}^{2} - 3x - 3x + x {}^{2} + 2 - 17x + 34 }{x \times (x - 2)} = 0$



$\frac{2x {}^{2} +2 - 17x + 34 }{x \times (x - 2)} = 0$



$\frac{2x {}^{2} + 36 - 17x}{x \times (x - 2)} = 0$



$2x {}^{2} + 36 - 17x = 0$

$2x {}^{2} - 17x + 36 = 0$



$x = \frac{ - ( - 17 ) + - \sqrt{( - 17) {}^{2} - 4 \times 2 \times 36 } }{2 \times 2}$



$x = \frac{17 + - \sqrt{289 - 288} }{4}$



$x = \frac{17 + \sqrt{1} }{4}$

$x = \frac{17 + - 1}{4}$

$means... \\ \\ \\ x = \frac{17 + 1}{4 } \\ \\ x = \frac{17 - 1}{4}$


$x1= \frac{9}{2 } \\ \\ x2 = 4$


$\mathcal{\orange{\bold{\star\:Madhura20}}}$