Solve: 10 x - 1 x = 3

10x − 1x = 3⇒ 10x2 − 1 = 3x⇒ 10x2 − 3x − 1 = 0⇒ 10x2 − 5x + 2x − 1 = 0⇒ 5x(2x − 1) + 1(2x − 1) = 0⇒ (2x − 1)(5x + 1) = 0∴ x = 12, x = −15

Solve: $10 x - \frac{1}{x} = 3 .$

10 x - \frac{1}{x} = 3 \Rightarrow 10 x^{2} - 1 = 3 x ⇒ 10 x^{2} - 3 x - 1 = 0 ⇒ 10 x^{2} - 5 x + 2 x - 1 = 0 ⇒ 5 x (2 x - 1) + 1 (2 x - 1) = 0 \Rightarrow (2 x - 1) (5 x + 1) = 0 ∴ x = \frac{1}{2}, x = - \frac{1}{5}