Question 304676
(z+7)/(z+3)=(z+1)/(z+7)+1

(z+7)/(z+3) - (z+1)/(z+7) = 1

A common denominator for the left side is (z+3)*(z+7). So we multiply the first term by (z+7)/(z+7) = 1 and the second term by (z+3)/(z+3) = 1 gives us:

(z+7)*(z+7)/(z+3)*(z+7) - (z+1)*(z+3)/(z+7)*(z+3) = 1

((z+7)^2 - (z+1)*(z+3))/((z+3)*(z+7)) = 1

(z^2 + 14z + 49 - (z^2 + 4z + 3))/(z^2 + 10z + 21) = 1
(10z + 46)/(z^2 + 10z + 21) = 1
Multiply both sides by z^2 + 10z + 21:
10z + 46 = z^2 + 10z + 21
z^2 - 25 = 0
(z+5)*(z-5) = 0

z = -5 or z = 5