Find all values of x satisfying the given conditions.
-$y _ { 1 } = \frac { 1 } { x + 5 } , y _ { 2 } = \frac { 1 } { x + 3 } , y _ { 3 } = \frac { - 2 } { x ^ { 2 } + 8 x + 15 }$, and the sum of $y _ { 1 }$ and 2 times $y _ { 2 }$ is $y 3$.
A) $\{ 0 \}$
B) $\{ - 5 \}$
C) $\{ 3 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

The given condition translates to $y_1 + 2y_2 = y_3$. Substituting the given expressions for $y_1$, $y_2$, and $y_3$ and simplifying does not yield a solution that satisfies the original equations, indicating that there are no values of $x$ that meet the given conditions.

Find All Values of X Satisfying the Given Conditions y1=1x+5,y2=1x+3,y3=−2x2+8x+15y _ { 1 } = \frac { 1 } { x + 5 } , y _ { 2 } = \frac { 1 } { x + 3 } , y _ { 3 } = \frac { - 2 } { x ^ { 2 } + 8 x + 15 }y1​=x+51​,y2​=x+31​,y3​=x2+8x+15−2​

Find All Values of X Satisfying the Given Conditions $y _ { 1 } = \frac { 1 } { x + 5 } , y _ { 2 } = \frac { 1 } { x + 3 } , y _ { 3 } = \frac { - 2 } { x ^ { 2 } + 8 x + 15 }$