Final answer:
To determine the restrictions for the equation (4x)/(x^(2)-2x-15)=(x+1)/(x+3), we need to find the values of x that will make the denominator(s) equal to zero. The restrictions for the equation are x cannot be equal to 5 and x cannot be equal to -3.
Step-by-step explanation:
To determine the restrictions for the equation (4x)/(x^(2)-2x-15)=(x+1)/(x+3), we need to find the values of x that will make the denominator(s) equal to zero. In this case, the denominators are x^(2)-2x-15 and x+3. To find the restrictions, we set the denominators equal to zero and solve for x.
Step 1:
Set the denominator x^(2)-2x-15 equal to zero:
x^(2)-2x-15=0
Step 2:
Factor the quadratic equation:
(x-5)(x+3)=0
Step 3:
Set each factor equal to zero and solve for x:
x-5=0: x=5
x+3=0: x=-3
Step 4:
The restrictions for the equation are x cannot be equal to 5 and x cannot be equal to -3.