Question

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

x+a/ax=b/x

Part 1. Show all work to solve for x in the equation and check the solution.
Part 2. Explain how to identify the extraneous solution and what it means.

Answer 1

Did you mean it the way you typed it, then by the order of operations....
x + 1x= b/x, since a/a = 1
2x = b/x
2x^2 = b
x^2 = √(b/2)
for extraneous roots, a can be any non-zero number, and b < 0

If you meant:
(x+a)/(ax) = b/x
x^2 + ax = abx
x^2 + ax - abx = 0
x^2 + x(a - ab) = 0

for extraneous roots the discriminant < 0
(a-ab)^2 - 4(1)(0) < 0
(a - ab)^2 < 0
but any square is ≥ 0, so no combination of a and b will produce extraneous roots

if you meant:
((x+a)/a)(x) = b/x
...

you try it