How can I change f(x) = (2x-1)/(x+2)f(x)=2x−1x+2 into the form A + B/(x+2)A+Bx+2 where A and B are both integers?
1 Answer
Aug 20, 2017
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)−4−1
=2(x+2)-5=2(x+2)−5
rArr(2(x+2)-5)/(x+2)=2-5/(x+2)⇒2(x+2)−5x+2=2−5x+2
color(blue)"As a check"As a check
2-5/(x+2)2−5x+2
=(2(x+2))/(x+2)-5/(x+2)=2(x+2)x+2−5x+2
=(2x+4-5)/(x+2)=(2x-1)/(x+2)larr" True"=2x+4−5x+2=2x−1x+2← True