Answer:
x = 3
Step-by-step explanation:
Use Angle bisector theorem (look at the picture)
[tex]\dfrac{24}{9x-9}=\dfrac{32}{6x+6}\qquad\text{cross multiply}\\\\24(6x+6)=32(9x-9)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(24)(6x)+(24)(6)=(32)(9x)+(32)(-9)\\\\114x+144=288x-288\qquad\text{subtract 144 from both sides}\\\\144x=288x-432\qquad\text{subtract}\ 288x\ \text{from both sides}\\\\-144x=-432\qquad\text{divide both sides by (-144)}\\\\x=3[/tex]
