How do you simplify #\frac { \frac { c + 4} { c ^ { 2} + 5c - 24} } { \frac { 2c ^ { 2} + 8c } { 2c ^ { 2} - 3c - 9} }#?

1 Answer
Tamir E.
Nov 19, 2017

#(2c+3)/(2c*(c+8))#

#c!=-4#
#c!=3#

Explanation:

#((c+4)/(c^2+5c-24))/((2c^2+8c)/(2c^2-3c-9))=#
#=((c+4)*(2c^2-3c-9))/((c^2+5c-24)*(2c^2+8c))=#

#(2c^2-3c-9)=(c-3)(2c+3)#
#(c^2+5c-24)=(c-3)(c+8)#

#=>#

#=((c+4)*(c-3)*(2c+3))/((c-3)*(c+8)*2c*(c+4))=#
#=((2c+3))/((c+8)*2c)#

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