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Veseljchak [2.6K]
3 years ago
9

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

Mathematics
2 answers:
In-s [12.5K]3 years ago
4 0
--Answer--

Any proposed solution of a rational equation that makes a denominator equal to the numerator is rejected.


Regards!I hope it helps you :)
Svetllana [295]3 years ago
4 0

Answer:

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 :  \frac{x}{x-4}=\frac{x}{x-4}+4

Now, solved the rational expression and check its proposed solution

\frac{x}{x-4}=\frac{x}{x-4}+4

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

Multiply both the sides by (x-4),

\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot\left ( \frac{x}{x-4}+4  \right )\\

Now, use the distributive property on Right hand side,

\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot \left ( \frac{x}{x-4} \right )+\left (x-4 \right )\cdot 4\\

Simplify the above expression,

x=x+4x-16

Combine like terms,

x-x-4x=-16

-4x=-16

Divide both sides by -4, we get

\frac{-4x}{-4}=\frac{-16}{-4}

x=4.

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: \frac{x}{x-4}=\frac{x}{x-4}+4

Substitute the value of <em>x</em>=4 in the original expression,

\frac{4}{4-4}=\frac{4}{4-4}+4

\frac{4}{0}=\frac{4}{0}+4

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












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