Solve the equation.
-$$\frac { 1 } { x } + \frac { 1 } { x - 3 } = \frac { x - 2 } { x - 3 }$$

Question

Quizplus · Accepted Answer

To solve the equation, combine the fractions on the left side by finding a common denominator, which is $x(x-3)$. This gives $\frac{x + (x-3)}{x(x-3)} = \frac{x-2}{x-3}$. Simplifying the numerator on the left gives $\frac{2x-3}{x(x-3)}$, which must be equal to $\frac{x-2}{x-3}$. Cross-multiplying gives $2x-3 = x(x-3) + 2(x-3)$, which simplifies to $2x-3 = x^2 - 3x + 2x - 6$, or $x^2 - 7x + 3 = 0$. Solving this quadratic equation using the quadratic formula or factoring (if possible) yields $x = 1$ as the only solution that does not result in division by zero or an invalid operation within the original equation.

Solve the Equation 1x+1x−3=x−2x−3\frac { 1 } { x } + \frac { 1 } { x - 3 } = \frac { x - 2 } { x - 3 }x1​+x−31​=x−3x−2​

Solve the Equation $\frac { 1 } { x } + \frac { 1 } { x - 3 } = \frac { x - 2 } { x - 3 }$