2. Solve for x . أحل المعادلة الثّالية $$ \frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12} $$ A. $$ \square $$ B. B. $$ \square $$ C. all real numbers جميع الأعداد الحققيةِّ D. no real solution لا يوجد حل في الأعداد الحقّيقَية

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Solve the equation $$ \frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2}{x+3}-\frac{3}{4-x}=\frac{2x-2}{x^{2}-x-12}$$
- step1: Find the domain:
  $$\frac{2}{x+3}-\frac{3}{4-x}=\frac{2x-2}{x^{2}-x-12},x \in \left(-\infty,-3ight)\cup \left(-3,4ight)\cup \left(4,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(\frac{2}{x+3}-\frac{3}{4-x}ight)\left(-x+4ight)\left(x+3ight)=\frac{2x-2}{x^{2}-x-12}	imes \left(-x+4ight)\left(x+3ight)$$
- step3: Simplify the equation:
  $$-1-5x=-2x+2$$
- step4: Move the expression to the left side:
  $$-5x+2x=2+1$$
- step5: Add and subtract:
  $$-3x=2+1$$
- step6: Add and subtract:
  $$-3x=3$$
- step7: Change the signs:
  $$3x=-3$$
- step8: Divide both sides:
  $$\frac{3x}{3}=\frac{-3}{3}$$
- step9: Divide the numbers:
  $$x=-1$$
- step10: Check if the solution is in the defined range:
  $$x=-1,x \in \left(-\infty,-3ight)\cup \left(-3,4ight)\cup \left(4,+\inftyight)$$
- step11: Find the intersection:
  $$x=-1$$
La solución de la ecuación es $$ x = -1 $$. Por lo tanto, la respuesta correcta es la opción A. $$ x = -1 $$.
La solución es $$ x = -1 $$.

2. Solve for x . أحل المعادلة الثّالية \[ \frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12} \] A. \( \square \) B. B. \( \square \) C. all real numbers جميع الأعداد الحققيةِّ D. no real solution لا يوجد حل في الأعداد الحقّيقَية

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