How do you combine #\frac { 5a } { a ^ { 2} - 2a + 1} + \frac { 2} { a ^ { 2} + a - 2}#?

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Answer 1 · 2017-03-23T10:55:53

#(5a^2+12a-2)/((a-1)^2(a+2))#

Adding of algebraic fractions is no different from arithmetic fractions.

Firstly you need the lowest common denominator. In order to find this with algebraic expressions, factorise the denominators first.

#(5a)/color(red)((a^2 -2a+1)) + 2/color(blue)((a^2 +a-2))#

#=(5a)/(color(red)((a-1)(a-1))) + 2/color(blue)((a+2)(a-1)#

There is a common factor of #(x-1)# in the denominators.
The LCM of the denominators is #color(red)((a-1)(a-1))color(blue)((a+2))#

Now make equivalent fractions with the new denominator:

#(5acolor(blue)((a+2))+2(color(red)(a-1)))/(color(red)((a-1)(a-1))color(blue)((a+2))#

#=(5a^2 +10a+2a-2)/((a-1)(a-1)(a+2))#

#(5a^2+12a-2)/((a-1)(a-1)(a+2))" "larr# numerator does not factor