Thread: Rational equation, rational expression, simplifying,

When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression? Please share an example.

Thanks in advance for your assistance.

Originally Posted by dkpeppard

When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression? Please share an example.

Thanks in advance for your assistance.

Hi dkpeppard,

To preserve the value of a rational expression it is necessary to do the denominator just what you did to the numerator.

Example:

You see, nothing changes.

To 'clear' the denominator of a rational equation, it is necessary to multiply each term by the LCD. As long as you are multipling both sides of the equation by the same thing, nothing changes.

Example:



The LCD is 28(x+2)

Multiply each side by 28(x+2)

Thank you for the quick and concise answer, Masters.