Question

Solve the equation:
3/x+2
+x-1
/x-5=2​

Answer 1

$\frac{3}{x + 2} + \frac{x - 1}{x - 5} = 2 \\ = > \frac{3(x - 5) + (x - 1)(x + 2)}{(x + 2)(x - 5)} = 2 \\ = > \frac{3x - 15 + {x}^{2} + 2x - x - 2 }{ {x}^{2} - 5x + 2x - 10} = 2 \\ = > \frac{ {x}^{2} + 4x - 17}{ {x}^{2} - 3x - 10 } = 2 \\ = > {x}^{2} + 4x - 17 = 2({x}^{2} - 3x - 10) \\ = > {x}^{2} + 4x - 17 = 2 {x }^{2} - 6x - 20 \\ = > {x}^{2} - 2 {x}^{2} + 4x + 6x - 17 + 20 = 0 \\ = > - {x}^{2} + 10x + 3 = 0 \\ = > {x }^{2} - 10x - 3 = 0 \\ here \: a = 1 \\ \: \: \: \: \: \: \: \: \: \: \: b \: = 10 \\ \: \: \: \: \: \: \: \: \: \: \: c \: = - 3 \\ so \: \: \\ \: \: x = \frac{ -b \sqrt[ + - ]{ {b}^{2} - 4ac} }{2a} \\ \: \: \: \: \: = \frac{ - 10 \sqrt[ - ]{ {10}^{2} - 4 \times 1 \times ( - 3)} }{2 \times 1} \\ \: \: \: \: \: = \frac{ - 10 \sqrt[ + - ]{100 + 12} }{2} \\ \: \: \: \: \: = \frac{ - 10 \sqrt[ + - ]{112} }{2} \\ \: \: \: \: \: = \frac{ - 10 ( + - )4 \sqrt{7} } {2} \\ \: \: \: \: \: = \frac{2( - 5 {( + - )2 \sqrt{7} } }{2} \\ \: \: \: \: \: = - 5( + - )2 \sqrt{7}$