College Algebra Tutorial 11

College Algebra
Tutorial 11: Complex Rational Expres
sions

WTAMU > Virtual Math Lab > College Algebra > Tutorial 11: Complex Rational Expressions

Step 1:   If needed, rewrite the numerator and denominator so that they are each a single fraction.

Combining only the numerator we get:

*Rewrite fractions with LCD of y

Combining only the denominator we get:

*Rewrite fractions with LCD of y

Putting these back into the complex fraction we get:

*Write numerator over denominator

AND

Step 3: If needed, simplify the rational expression.

*Rewrite div. as mult. of reciprocal

*Divide out a common factor of y

*Excluded values of the original den.

Note that the values that would be excluded from the domain are 0 and -1/2.  These are the values that make the original denominators equal to 0.

Step 1: Multiply the numerator and denominator of the overall complex fractions by the LCD of the smaller fractions.

The denominators of the numerator's fractions have the following factors:

The denominators of the denominator's fractions  have the following factors:

Putting all the different factors together and using the highest exponent, we get the following LCD for all the small fractions:

Multiplying numerator and denominator by the LCD we get:

*Mult. num. and den. by x(x +3)

Step 2: If needed, simplify the rational expression.

*Factor the GCF of 2
*No common factors to divide out

*Excluded values of the original den.

Note that the values that would be excluded from the domain are 0, -3 and -7/2.  These are the values that make the original denominators equal to 0.