SOLUTION: I need to solve a rational equation that simplifies to a quadratic equation: (z+7)/(z+3)=(z+1)/(z+7)+1

Question 304676: I need to solve a rational equation that simplifies to a quadratic equation:
(z+7)/(z+3)=(z+1)/(z+7)+1
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
(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

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