Checking Solutions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Someone solved xx−2=2x−2\frac{x}{x-2} = \frac{2}{x-2} and got x=2x = 2. Is this valid?

Solution

  1. 1
    At x=2x = 2, the denominator x−2=0x - 2 = 0. Division by zero is undefined.
  2. 2
    x=2x = 2 is extraneous—the equation has no solution.

Answer

No—x=2x = 2 makes the denominator zero. No solution.
Always check that solutions don't violate domain restrictions. Values making any denominator zero are excluded.

About Checking Solutions

Checking solutions means substituting candidate values back into the original condition to verify they satisfy it.

Learn more about Checking Solutions →

More Checking Solutions Examples

Example 1 easy

Check whether [formula] is a solution of [formula].

Example 2 medium

Solve [formula] and check for extraneous solutions.

Example 3 easy

Is [formula] a solution of [formula]?

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