Any proposed solution of a rational equation that causes a denominator to equal is rejected.

Any proposed solution of a rational equation that causes a denominator to equal __ZERO__ is rejected.

Step-by-step explanation:

We will show this statement is true by an example:

Consider the expression :  

Now, solved the rational expression and check its proposed solution

x cannot equal to 4, as it makes  both denominators equal to zero.

Multiply both the sides by (x-4),

Now, use the distributive property on Right hand side,

Simplify the above expression,

Combine like terms,

Divide both sides by -4, we get

.

As we know that x cannot equal to 4, replacing x=4 in the original expression causes the denominator equal to 0.

Check the solution:

Substitute the value of x=4 in the original expression,

Thus, 4 must be rejected as the solution, and the solution set is only 0.