Challenge Evaluate the sum

anemone

Paris la ville de l'amour
Staff member
Administrator
Moderator
Math Helper
Jan 28, 2018
181
219
43
Given that \(\displaystyle abx^2=(a-b)^2(x+1)\).

Find \(\displaystyle 1+\dfrac{4}{x}+\dfrac{4}{x^2}\).
 
  • Like
Reactions: MarkFL

MarkFL

La Villa Strangiato
Staff member
Administrator
Moderator
Math Helper
Jan 25, 2018
3,487
4,264
113
St. Augustine
I would begin by writing:

\(\displaystyle 1+\frac{4}{x}+\frac{4}{x^2}=1+4\frac{x+1}{x^2}=1+4\frac{ab}{(a-b)^2}=\left(\frac{a+b}{a-b}\right)^2\)
 
  • Like
Reactions: anemone

anemone

Paris la ville de l'amour
Staff member
Administrator
Moderator
Math Helper
Jan 28, 2018
181
219
43
Bravo, Mark! (Cool)
 
  • Like
Reactions: MarkFL