Solve the following mathematical problems:

solve the equation: $\frac{3}{x + 2} + \frac{x + 1}{x - 5} = 2$ (Equation)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$\frac{3}{x + 2} + \frac{x - 1}{x - 5} = 2 \Rightarrow \frac{3 (x - 5) + (x - 1) (x + 2)}{(x + 2) (x - 5)} = 2 \Rightarrow \frac{3 x - 15 + x^{2} + 2 x - x - 2}{x^{2} - 5 x + 2 x - 10} = 2 \Rightarrow \frac{x^{2} + 4 x - 17}{x^{2} - 3 x - 10} = 2 \Rightarrow 2 x^{2} - 6 x - 20 = x^{2} + 4 x - 17 \Rightarrow x^{2} - 10 x - 3 = 0 N o w u \sin g a x^{2} + b x + c = 0 H e r e, a = 1; b = - 10; c = - 3 W e k n o w, x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 \times 1 \times (- 3)}}{2 \times 1} \Rightarrow x = \frac{10 \pm \sqrt{100 + 12}}{2} \Rightarrow x = \frac{10 \pm \sqrt{112}}{2} \Rightarrow x = \frac{10 \pm \sqrt{16 \times 7}}{2} \Rightarrow x = \frac{10 \pm 4 \sqrt{7}}{2} \Rightarrow x = \frac{2 (5 \pm 2 \sqrt{7})}{2} ∴ x = 5 \pm 2 \sqrt{7}$