Simplify Rational Expressions Tutorial
Creator of Tutorial: iYuko

Question

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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$$(3x+2)\div(x+4) ~~or~~\frac{ 3x+2 }{ x+4 }$$

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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.

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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:

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BASIC RULE OF FRACTIONS:

For any polynomials a, b, c  $$(b \neq0~~\And~~c \neq0),$$$$\frac{ ac }{ bc }=\frac{ a }{ b }$$