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Question 169942This question is from textbook Introductory Algebra
: Divide and, if possible, simplify
z^2 + 8z + 16/z^2 + 13z + 36 divided by z^2 + 4z/z^2 + 15z + 54This question is from textbook Introductory Algebra
: Divide and, if possible, simplify
z^2 + 8z + 16/z^2 + 13z + 36 divided by z^2 + 4z/z^2 + 15z + 54
Answer by jim_thompson5910(9929) About Me  (Show Source):
You can put this solution on YOUR website!

((z^2+8z+16)/(z^2+13z+36))/((z^2+4z)/(z^2+15z+54)) Start with the given expression.


((z^2+8z+16)/(z^2+13z+36))((z^2+15z+54)/(z^2+4z)) Multiply the first fraction (z^2+8z+16)/(z^2+13z+36) by the reciprocal of the second fraction (z^2+4z)/(z^2+15z+54).


(((z+4)(z+4))/(z^2+13z+36))((z^2+15z+54)/(z^2+4z)) Factor z^2+8z+16 to get (z+4)(z+4).


(((z+4)(z+4))/((z+9)(z+4)))((z^2+15z+54)/(z^2+4z)) Factor z^2+13z+36 to get (z+9)(z+4).

(((z+4)(z+4))/((z+9)(z+4)))(((z+9)(z+6))/(z^2+4z)) Factor z^2+15z+54 to get (z+9)(z+6).


(((z+4)(z+4))/((z+9)(z+4)))(((z+9)(z+6))/(z(z+4))) Factor z^2+4z to get z(z+4).


((z+4)(z+4)(z+9)(z+6))/(z(z+9)(z+4)(z+4)) Combine the fractions.


(highlight((z+4))highlight((z+4))highlight((z+9))(z+6))/(z*highlight((z+9))highlight((z+4))highlight((z+4))) Highlight the common terms.

(cross((z+4))cross((z+4))cross((z+9))(z+6))/(z*cross((z+9))cross((z+4))cross((z+4))) Cancel out the common terms.


(z+6)/(z) Simplify.


So ((z^2+8z+16)/(z^2+13z+36))/((z^2+4z)/(z^2+15z+54)) simplifies to (z+6)/(z).


In other words, ((z^2+8z+16)/(z^2+13z+36))/((z^2+4z)/(z^2+15z+54))=(z+6)/(z) where z<>-9, z<>-6, z<>-4, or z<>0.