Easy Algebra Step-by-Step

148 Easy Algebra Step-by-Step

Step 4. Review the main results.

5

4

41

4

541

4

1

4

x^224 x xx^2244 x^2 x^1

()x^1

−

()x^1

=

4 x −

()x^1

=

−

()x^1

=

()()xx+ 111 ( ))

()()

=

()−

4 ( ++^4

Adding (or Subtracting) Algebraic Fractions, Unlike Denominators

To add (or subtract) algebraic fractions that have unlike denominators,

(1) factor each denominator completely; (2) fi nd the least common denomi-

nator (LCD), which is the product of each prime factor the highest number

of times it is a factor in any one denominator; (3) using the fundamental

principle, write each algebraic fraction as an equivalent fraction having the

common denominator as a denominator; and (4) add (or subtract) as for like

denominators.

Note: A prime factor is one that cannot be factored further.

Problem Compute as indicated.

a.

3

(^242)
x
x
x
− x

• −
  b.^21
  322
  x
  x
  x
  − x
  −


• 
  

  Solution
  a.^3
  (^242)
  x
  x
  x
  − x

  
  


• 
  

  −
  Step 1. Factor each denominator completely.
  3
  (^242)
  x
  x
  x
  − x

  
  

+

=

()+ ()

+

()−

3

)( −

x

+ ))((

x

Step 2. Find the LCD.

LCD = ()x+ )(()xx−