144 Easy Algebra Step-by-Step

Solution

a. xx

x

x

x

2

2

21 x

4

36 x

-^1

⋅

−

Step 1. Factor all numerators and denominators completely.

xx

x

x

x

2

2

21 x

4

36 x

• 1

⋅

−

=

()()

()+ ()

⋅

()

()−

− )(

+ )(

))(( −

))(( −

3 ( −

Step 2. Divide out common numerator and denominator factors.

=

()()()

()+ ()()

⋅

()()

()()−−

−− )(

+ )(

))(( −

))(( −−

3 ( −−

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.

= ()

()+

(^3) ( −
Step 4. Review the main results.
xx
x
x
x
2
2
21 x
4
36 x

• 1

⋅

−

(^331) xx

()()xx 11 ()xx 1
()x+ 2 ()()xxxx 22

⋅

()()xxxx 22

()()xx−− 11

=

( ))

()+

b.^24

3

9

56

2

2

x

x

x

− xx^25

⋅ −

+ 55

Step 1. Factor all numerators and denominators completely.

24

3

9

56

2

2

x

x

x

− xx 5

⋅

−

+ 55

=

()

− ()

⋅

()+ ()

()+ ()

2 ( +

1 ( −

)( −

)( +

+ ))((

+ ))((

When you are multiplying algebraic fractions,

if a numerator or denominator does not

factor, enclose it in parentheses. Forgetting

the parentheses can lead to a mistake.

Be careful! Only divide out factors.

When you multiply algebraic fractions,

you can leave your answer in factored

form. Always double-check to make sure

it is in completely reduced form.

Write all polynomial factors with the variable

terms fi rst, so that you can easily recognize

common factors.