How do you combine #-10/(z^2-6z+5)+15/(z^2-4z-5)#?

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Answer 1 · 2017-06-21T20:27:53

#5/(z^2 -1)#

#-10/(z^2 - 6z + 5) + 15/(z^2 - 4z -5)#

factorise denominator,

# = -10/((z- 1)(z - 5)) + 15/((z + 1)(z -5))#

equalize the denominator,

# = -(10 (z + 1))/((z- 1)(z - 5)(z + 1)) + (15(z - 1))/((z + 1)(z -5)(z - 1))#

#= (-10z - 10)/((z- 1)(z - 5)(z + 1)) + (15z - 15)/((z + 1)(z -5)(z - 1))#

since it has a same denominator, combine all together and simplify,

#= (-10z - 10 + 15z -15)/((z- 1)(z - 5)(z + 1)) #

#= (5z -25)/((z- 1)(z - 5)(z + 1)) #

#= (5cancel((z -5)))/((z- 1)cancel((z - 5))(z + 1)) #

#= (5)/((z- 1)(z + 1)) #

#= 5/(z^2 -1)#