Answer:
AB+AC
Step-by-step explanation:
Given: [tex] \frac{BX}{XC}=\frac{AB}{AC}[/tex]
To determine: (BX+XC) : XC =? : AC
We need to find ? here
We have
[tex] \frac{BX}{XC}=\frac{AB}{AC}[/tex]
Add 1 both sides
[tex] \frac{BX}{XC}+1=\frac{AB}{AC}+1[/tex]
Taking LCM and simplify it
[tex]\frac{BX+XC}{XC}=\frac{AB+AC}{AC}[/tex]
We can write fraction as ration
(BX+XC) : XC= (AB+AC) : AC
At place of "?" we get AB+AC
Thus, option 3 is correct. AB+AC
