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Math Help - Rational equation, rational expression, simplifying,

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by dkpeppard View Post
    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:  \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
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  3. #3
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    Thank you for the quick and concise answer, Masters.
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