# Thread: Rational equation, rational expression, simplifying,

1. ## 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.

2. 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.

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: $\frac{1}{2} \cdot \frac{3}{3} \cdot \frac{a^2}{a^2}=\frac{3a^2}{6a^2}=\frac{1}{2}$

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:

$\frac{9}{28}+\frac{3}{x+2}=\frac{3}{4}$

The LCD is 28(x+2)

Multiply each side by 28(x+2)

$28(x+2)\left(\frac{9}{28}+\frac{3}{x+2}\right)=28( x+2)\left(\frac{3}{4}\right)$

$(9x+18)+84=21x+42$

$9x+102=21x+42$

$60=12x$

$5=x$

3. Thank you for the quick and concise answer, Masters.