Solve the equation.
-$x - \frac { 10 } { x - 1 } = 6 - \frac { 4 x } { x - 1 }$

Question

Quizplus · Accepted Answer

To solve the equation $x - \frac { 10 } { x - 1 } = 6 - \frac { 4 x } { x - 1 }$, we first find a common denominator, which is $x - 1$, and rewrite the equation as $\frac{x(x - 1) - 10}{x - 1} = \frac{6(x - 1) - 4x}{x - 1}$. Simplifying both sides gives $\frac{x^2 - x - 10}{x - 1} = \frac{6x - 6 - 4x}{x - 1}$, which simplifies further to $\frac{x^2 - x - 10}{x - 1} = \frac{2x - 6}{x - 1}$. Multiplying both sides by $x - 1$ to eliminate the denominator, we get $x^2 - x - 10 = 2x - 6$. Rearranging terms gives $x^2 - 3x - 4 = 0$, which factors to $(x - 4)(x + 1) = 0$. Therefore, the solutions are $x = 4$ and $x = -1$.

Solve the Equation x−10x−1=6−4xx−1x - \frac { 10 } { x - 1 } = 6 - \frac { 4 x } { x - 1 }x−x−110​=6−x−14x​

Solve the Equation $x - \frac { 10 } { x - 1 } = 6 - \frac { 4 x } { x - 1 }$