How do you subtract #\frac { 8a - 3} { 3a ^ { 2} + 2a - 5} - \frac { 5a - 8} { 3a ^ { 2} + 2a - 5}#?

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Answer 1 · 2016-11-08T08:58:07

#=1/((a-1))#

The basics in algebraic fractions are the same as in arithmetic fractions.. In this case, subtracting.

There must be a common denominator. The denominator in both fractions is the same, so you can just subtract the numerators:

#(8a-3)/(3a^2+2a-5) - (5a-8)/(3a^2+2a-5)#

#= (8a-3color(blue)(-)(5a-8))/((3a^2+2a-5))" "larr# note the minus sign!

#= (8a-3color(blue)(-5a+8))/((3a^2+2a-5))" "larr# factorise the denominator

#=((3a+5))/((3a+5)(a-1)#

#=cancel((3a+5))/(cancel((3a+5))(a-1)#

#=1/((a-1))#