How do you solve #1 + 8/(x - 5) = 3/x# and find any extraneous solutions?
1 Answer
There are no Real solutions, but there are Complex solutions:
#x = +-sqrt(15)i#
Explanation:
Given:
#1+8/(x-5) = 3/x#
Note that neither
Multiply both sides by
#x + (8x)/(x-5) = 3#
Multiply both sides by
#x(x-5) + 8x = 3(x-5)#
Expand both sides to get:
#x^2-5x+8x = 3x-15#
which simplifies to:
#x^2+3x = 3x-15#
Subtract
#x^2 = -15#
This has no Real solutions since
If we are interested in Complex solutions, then add
#0 = x^2+15 = x^2 - (sqrt(15)i)^2 = (x-sqrt(15)i)(x+sqrt(15)i)#
where
Hence solutions