Easy Algebra Step-by-Step

Rational Expressions 145

Step 2. Divide out common numerator and denominator factors.

=

()()

− ()()

⋅

()()+ ()()

()()+ ()()

(^2) ( ++
1 ( −−

)( −−

)( ++

++ ))((

++ ))((

Step 3. Multiply the remaining numerator factors to get the numerator of

the answer, and multiply the remaining denominator factors to get

the denominator of the answer.

=

−

=−

2

1

2

Step 4. Review the main results.

24

3

9

56

2

1

2

2

2

x

x

x

− xx 5

⋅

−

+ 55

=

()()xx 22

− 1 ()()xx 33

⋅

()()xx+ 333 ()()xx 33

()()xx+ 222 ()()xx 33

=−

Dividing Algebraic Fractions

To divide algebraic fractions, multiply the fi rst algebraic fraction by the

reciprocal of the second algebraic fraction (the divisor).

Problem Find the quotient:

xx

xx

xx

x

2

2

2

2

21 x

6

32 x

− 4

÷

3 x

−

.

Solution

Step 1. Change the problem to multiplication by the reciprocal of the

divisor.

xx

xx

xx

x

2

2

2

2

21 x

6

32 x

− 4

÷

3 x

−

=

−

⋅

xx −

xx

x

xx−

2

2

2

2

21 x+

6

4

32 x+

Step 2. Factor all numerators and denominators completely.

=

()()

()()

⋅

()+ ()

()()

− )(

− )(

+ )(

− )(

))(( −

))(( +

))(( −

))(( −