How do you solve #1/(t^3+t^2-25t-25) + 2/(t^2-25) - 3/(t^2+6t+5)=0#?

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Answer 1 · 2016-12-10T15:06:48

Factor the denominators to determine the LCD (Least Common Denominators)..

#t^3 + t^2 - 25t - 25 = t^2(t + 1) - 25(t + 1) = (t^2 - 25)(t + 1) = (t + 5)(t- 5)(t + 1)#

#t^2 - 25 = (t + 5)(t - 5)#

#t^2 + 6t + 5 = (t + 5)(t + 1)#

#:.# The LCD is #(t + 5)(t + 1)(t - 5)#.

#1/((t + 5)(t+ 1)(t - 5)) + (2(t - 1))/((t + 5)(t + 1)(t - 5)) - (3(t - 5))/((t + 5)(t + 1)(t - 5)) = 0#

You can eliminate the denominators now.

#1 + 2t - 2 - 3t + 15= 0#

#-t = -12#

#t = 12#

The restrictions are #t!= +-5, -1#, so #t = 12# is a valid solution.

Hopefully this helps!