Easy Algebra Step-by-Step

Rational Expressions 143

Step 4. Use the fundamental principle to reduce the fraction.

x

x

()()xx+ ()x

()()xx+ ()x

=

−

+

)(x−

)(x+

1

1

g.

x y

xy

()a−b y()aba

+

Step 1. Factor the numerator and denominator polynomials completely.

x by

xy

y

y

(a b ()ab()xy()ab

()xy

b

+

=

y)(a

Step 2. Determine the GCF for (x+y)(a − b) and (x+y).

GCF = (x+y)

Step 3. Use the fundamental principle to reduce the fraction.

ab ab

ab

()()xyx+ ( )

()()xyx+

= =a

1

Multiplying Algebraic Fractions

To multiply algebraic fractions, (1) factor all numerators and denominators

completely, (2) divide numerators and denominators by their common fac-

tors (as in reducing), and (3) multiply the remaining numerator factors to get

the numerator of the answer and multiply the remaining denominator fac-

tors to get the denominator of the answer.

Problem Find the product.

a. xx

x

x

x

2

2

21 x

4

36 x

-^1

⋅

−

b.

24

3

9

56

2

2

x

x

x

− xx^25

⋅

−

+ 55