Solve the equation. $\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }$
A) x = -5, x = 8
B) x = 5, x = 8
C) x = 5, x = $-$ 8

Question

Quizplus · Accepted Answer

To solve the equation, first, we need to find the common denominator of the left side of the equation:
$$\frac{x(x+7)}{(x-3)(x+7)}-\frac{4(x-3)}{(x-3)(x+7)}=\frac{52}{x^2+4x-21}$$
Simplifying,
$$\frac{x(x+7)-4(x-3)}{(x-3)(x+7)}=\frac{52}{(x-3)(x+7)}$$
$$\frac{x^2+3x-28}{(x-3)(x+7)}=\frac{52}{(x-3)(x+7)}$$
$$(x^2+3x-28)-52=0$$
$$(x-5)(x+8)=0$$
Thus, the solutions are $x=5$ and $x=-8$, so the answer is C.

Solve the Equation xx−3−4x+7=52x2+4x−21\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }x−3x​−x+74​=x2+4x−2152​

Solve the Equation $\frac { x } { x - 3 } - \frac { 4 } { x + 7 } = \frac { 52 } { x ^ { 2 } + 4 x - 21 }$