How do you simplify #\frac { m - 9} { m ^ { 3} - 1} - \frac { 8} { 1- m ^ { 3} }#?

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Answer 1 · 2017-09-13T11:56:52

#=1/(m^2+m+1)#

In order to add or subtract fractions, the denominators must be the same.

Note that# -(a-b) = (+b-a) " "larr# do a 'switch-round'

#(m-9)/(m^3-1) - 8/(1-m^3) = (m-9)/(m^3-1) + 8/(m^3 -1)#

#=(m-9+8)/(m^3-1)#

#=((m-1))/((m-1)(m^2+m+1))" "(larr "simplify")/(larr" factorise the denominator")#

#=(cancel((m-1)))/(cancel((m-1))(m^2+m+1))#

#=1/(m^2+m+1)#

Note: to factorise the difference of cubes:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#