How can I change f(x) = (2x-1)/(x+2)f(x)=2x1x+2 into the form A + B/(x+2)A+Bx+2 where A and B are both integers?

1 Answer
Aug 20, 2017

2-5/(x+2)25x+2

Explanation:

"using "(x+2)" as a factor in the numerator"using (x+2) as a factor in the numerator

"consider the numerator"consider the numerator

2(x+2)color(magenta)(-4)-12(x+2)41

=2(x+2)-5=2(x+2)5

rArr(2(x+2)-5)/(x+2)=2-5/(x+2)2(x+2)5x+2=25x+2

color(blue)"As a check"As a check

2-5/(x+2)25x+2

=(2(x+2))/(x+2)-5/(x+2)=2(x+2)x+25x+2

=(2x+4-5)/(x+2)=(2x-1)/(x+2)larr" True"=2x+45x+2=2x1x+2 True