Simplify Rational Expressions. Tutorial! Check it Out!
Recall that a rational number is a number that can be written as 1 integer divided by another integer such as \[3\div4 ~~or~~\frac{ 3 }{ 4 }\]A rational expression is an algebraic expression divided by another algebraic expression. Such as\[(3x+2)\div(x+4) ~~or~~\frac{ 3x+2 }{ x+4 }\]
The last fraction is sometimes called a fractional algebraic expression. There is a special restriction for all fractions, including fractional algebraic expressions. The denominator of the fraction cannot be 0. For example, in the expression \[\frac{ 3x+2 }{ x+4}\] The denominator cannot be 0. Therefore, the value of x cannot be -4.
We discovered that fractions can be simplified in the following way. \[\frac{ 15 }{ 25 }~=~\frac{ 3\times5 }{ 5\times5 }~=~\frac{ 3 }{ 5}\]This is sometimes referred to as the basic rule of fractions. And can be stated as follows:
BASIC RULE OF FRACTIONS: For any polynomials a, b, c \[(b \neq0~~\And~~c \neq0),\]\[\frac{ ac }{ bc }=\frac{ a }{ b }\]
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nice job there
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If I left something out, feel free to comment. :)
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Great works :)
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