How do you solve #\frac { 1} { s } + \frac { s } { s + 2} = 1#?

1 Answer
EZ as pi
Feb 23, 2017

#s = 2.732 " or "s = -0.732#

Explanation:

We have an equation with fractions, so we can get rid of the fractions. Multiply each term by the LCM of the denominators which in this case is #color(blue)(s(s+2))#

#(color(blue)(s(s+2))xx1)/s + (color(blue)(s(s+2))xx3)/(s+2) = color(blue)(s(s+2)) xx 1#

Cancel the denominators:

#(cancels(s+2)xx1)/cancels + (scancel((s+2))xx3)/cancel((s+2)) = color(blue)(s(s+2)) xx 1#

This leaves:

#s+2+3s = s^2+2s" "larr# simplify

#0 = s^2-2s-2" "larr# solve by completing the square

#s^2 -2s color(red)(+1) = 2color(red)(+1)#

#(s-1)^2 = 3#

#s-1 = +-sqrt3#

#s = sqrt3 +1 = 2.732#

#s = -sqrt3 +1 = -0.732#

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