Rational Expressions – Equivalent Forms

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Presentation transcript:

Rational Expressions – Equivalent Forms Here is the rule : You are allowed to MULTIPLY OR DIVIDE the numerator and denominator of a fraction by the SAME constant or variable

Rational Expressions – Equivalent Forms Here is the rule : You are allowed to MULTIPLY OR DIVIDE the numerator and denominator of a fraction by the SAME constant or variable ADDING / SUBTRACTING the numerator and denominator of a fraction by the SAME constant or variable DOES NOT create an equivalent fraction !!!

Rational Expressions – Equivalent Forms Here is the rule : You are allowed to MULTIPLY OR DIVIDE the numerator and denominator of a fraction by the SAME constant or variable ADDING / SUBTRACTING the numerator and denominator of a fraction by the SAME constant or variable DOES NOT create an equivalent fraction !!! When the fractions are simple, cross multiplying will quickly check for equivalence

Rational Expressions – Equivalent Forms Example # 1 : Are these fractions equivalent ?

Rational Expressions – Equivalent Forms Example # 1 : Are these fractions equivalent ? No, if I cross multiply I do not get a true statement…

Rational Expressions – Equivalent Forms Example # 2 : Are these fractions equivalent ?

Rational Expressions – Equivalent Forms Example # 2 : Are these fractions equivalent ? YES, because I can MULTIPLY both numerator and denominator by the same thing to get my result…

Rational Expressions – Equivalent Forms Example # 2 : Are these fractions equivalent ? YES, because I can CROSS MULTIPLY and get an equivalent statement

Rational Expressions – Equivalent Forms Example # 3 : Are these fractions equivalent ?

Rational Expressions – Equivalent Forms Example # 3 : Are these fractions equivalent ? YES, because I can cancel the ( b + 3 )… anything over itself = 1

Rational Expressions – Equivalent Forms Example # 4 : Are these fractions equivalent ?

Rational Expressions – Equivalent Forms Example # 4 : Are these fractions equivalent ? NO !!! You can not ADD / SUBTRACT the same thing from the numerator / denominator and get an equivalent form…