Download Extraneous Solutions

Extraneous Solutions
Extraneous Solutions
A proposed solution that is not a solution of the original
equation. These solutions arise from the solution method,
but do not satisfy the original equation.
Example One: Solve

5−𝑥−1=𝑥
5  x 1  x
5  x2  x  1
2
5  x   x  1
2
5  x  x  2x 1
2
0  x  3x  4
0   x  4  x  1
x  4 or 1

Always check your
answer(s):
x  4 :
5  4  1  4
9  1  4
2  4
Since -4 does not satisfy the original
equation, it is an extraneous solution.
x  1:
5 1 1  1
4 1  1
11
Since 1 does satisfy the original equation,
it is a solution.
Extraneous Solutions
A proposed solution that is not a solution of the original
equation. These solutions arise from the solution method,
but do not satisfy the original equation.
Example Two: Solve
1
x
 2
x 1 x 1
x  x  x 1
2
2
 x  1
x 1
1
𝑥−1
=
𝑥
𝑥 2 −1
Always check your
answer(s):
1
11
1
0
 1211
 10
Since you can not divide by 0, 1 does
not satisfy the original equation. It is
an extraneous solution.
Since all solutions are extraneous, there
are No Solutions to this equation.