Solve the equation.
-$$\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }$$
A) $\varnothing$
B) $\{ 6 , - 8 \}$
C) $\{ - 6,8 \}$
D) $\{ - 12,8 \}$

Question

Quizplus · Accepted Answer

To solve the equation, first get a common denominator and then solve for $x$. The equation is $\frac{10}{x-2} = 1 + \frac{12}{x+2}$. To simplify, multiply both sides by the common denominator $(x-2)(x+2)$ to get rid of the fractions: $10(x+2) = (x-2)(x+2) + 12(x-2)$. Simplifying further gives $10x + 20 = x^2 - 4 + 12x - 24$, which simplifies to $x^2 + 2x - 48 = 0$. Factoring this quadratic equation gives $(x-6)(x+8) = 0$, leading to the solutions $x = 6$ and $x = -8$.

Solve the Equation 10x−2=1+12x+2\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }x−210​=1+x+212​

Solve the Equation $\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }$