Given that abx^2=(a-b)^2(x+1). Find 1+\dfrac{4}{x}+\dfrac{4}{x^2}.

anemone Paris la ville de l'amour Staff member Administrator Moderator Math Helper Jan 28, 2018 181 219 43 Nov 9, 2018 #1 Given that \(\displaystyle abx^2=(a-b)^2(x+1)\). Find \(\displaystyle 1+\dfrac{4}{x}+\dfrac{4}{x^2}\). Reactions: MarkFL

Given that \(\displaystyle abx^2=(a-b)^2(x+1)\). Find \(\displaystyle 1+\dfrac{4}{x}+\dfrac{4}{x^2}\).

MarkFL La Villa Strangiato Staff member Administrator Moderator Math Helper Jan 25, 2018 3,487 4,264 113 St. Augustine Nov 9, 2018 #2 I would begin by writing: \(\displaystyle 1+\frac{4}{x}+\frac{4}{x^2}=1+4\frac{x+1}{x^2}=1+4\frac{ab}{(a-b)^2}=\left(\frac{a+b}{a-b}\right)^2\) Reactions: anemone

I would begin by writing: \(\displaystyle 1+\frac{4}{x}+\frac{4}{x^2}=1+4\frac{x+1}{x^2}=1+4\frac{ab}{(a-b)^2}=\left(\frac{a+b}{a-b}\right)^2\)

anemone Paris la ville de l'amour Staff member Administrator Moderator Math Helper Jan 28, 2018 181 219 43 Nov 9, 2018 #3 Bravo, Mark! Reactions: MarkFL