Wie beurteilen Sie # frac {3} {x + 1} + frac {2x - 5} {x ^ {2} - 3x - 4} #?

Antworten:

# (5x-17) / ((x + 1) (x-4)) #

Erläuterung:

Wir haben,# x ^ 2-3x-4 = x ^ 2-4x + x-4 = x (x-4) + 1 (x-4) = (x + 1) (x-4) #
So,
# 3 / (x + 1) + (2x-5) / (x ^ 2-3x-4) = 3 / (x + 1) + (2x-5) / ((x + 1) (x-4) ) #
# = (3 (x-4)) / ((x + 1) (x-4)) + (2x-5) / ((x + 1) (x-4)) #
# = (3 (x-4) + 2x-5) / ((x + 1) (x-4)) = (3x-12 + 2x-5) / ((x + 1) (x-4)) = (5x-17) / ((x + 1) (x-4)) = (5x-17) / (x ^ 2-3x-4) #