Solve the equation.
-$$\frac { - 3 } { x - 7 } = \frac { 6 } { x - 14 } - \frac { - 21 } { x ^ { 2 } - 21 x + 98 }$$
A) $\{ 7,14 \}$
B) $\{ 14 \}$
C) $\{ 7 \}$
D) no solution

Question

Quizplus · Accepted Answer

The equation involves fractions with variables in the denominators. The denominators $x-7$, $x-14$, and $x^2-21x+98$ suggest potential restrictions on $x$. Specifically, $x^2-21x+98$ can be factored into $(x-7)(x-14)$, indicating that both 7 and 14 make at least one denominator zero, leading to division by zero, which is undefined. Therefore, there are no values of $x$ that satisfy the equation without causing division by zero.

Solve the Equation −3x−7=6x−14−−21x2−21x+98\frac { - 3 } { x - 7 } = \frac { 6 } { x - 14 } - \frac { - 21 } { x ^ { 2 } - 21 x + 98 }x−7−3​=x−146​−x2−21x+98−21​

Solve the Equation $\frac { - 3 } { x - 7 } = \frac { 6 } { x - 14 } - \frac { - 21 } { x ^ { 2 } - 21 x + 98 }$