Find all values of x satisfying the given conditions.
-$y _ { 1 } = \frac { 6 } { x + 3 } , y _ { 2 } = \frac { 8 } { x - 3 } , y _ { 3 } = \frac { 14 } { x ^ { 2 } - 9 }$, and $y _ { 1 } - y _ { 2 } = y _ { 3 }$
A) $\{ - 28 \}$
B) $\{ 28 \}$
C) $\{ \sqrt { 43 } \}$
D) $\{ 56 \}$

Question

Quizplus · Accepted Answer

Substituting $y_1$ and $y_2$ into the equation $y_1 - y_2 = y_3$, we get $\frac{6}{x+3} - \frac{8}{x-3} = \frac{14}{x^2-9}$. Simplifying the equation by finding a common denominator and solving for $x$ yields $x = -28$.

Find All Values of X Satisfying the Given Conditions y1=6x+3,y2=8x−3,y3=14x2−9y _ { 1 } = \frac { 6 } { x + 3 } , y _ { 2 } = \frac { 8 } { x - 3 } , y _ { 3 } = \frac { 14 } { x ^ { 2 } - 9 }y1​=x+36​,y2​=x−38​,y3​=x2−914​

Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { 6 } { x + 3 } , y _ { 2 } = \frac { 8 } { x - 3 } , y _ { 3 } = \frac { 14 } { x ^ { 2 } - 9 }$