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Title: Algebra _ Simplification of rational expressions
Description: Algebra _ Simplification of rational expressions Step 1: Factor the numerator and the denominator. Step 2: List restricted values. Step 3: Cancel common factors. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.
Description: Algebra _ Simplification of rational expressions Step 1: Factor the numerator and the denominator. Step 2: List restricted values. Step 3: Cancel common factors. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.
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Algebra
Simplification of rational expressions
1
...
3
...
5
...
x2 + 7x + 12
x2 + 4x + 3
Simplify:
x 2 + 7x + 12
Solution:
7
...
Simplify:
x2 + 4x + 3
(x + 3) (x + 4)
x 2 6x + 8
x2 – 3x + 2
(x + 3) (x + 1)
=
4x 2 – 13x + 3
4x 1
(x – 4) (x – 2)
x–4
=
(x – 1) (x – 2)
x1
=
(4x – 1) (x – 3)
4x 1
= (x – 3)
( x – 1) ( x 2 ) ( x2 – x – 72)
Simplify:
(x – 9) ( x2 + x – 2)
(x – 2) ( x + 8)
(x –1) ( x 2 ) (x – 9) (x + 8)
Simplify:
x+1
4x 2 – 13x + 3
4x 1
Solution: =
10
...
=
( x – 9 ) (x + 2) (x – 1)
=
x+2
2x4 – 162
(x + 9) (2x 6)
2
2x 4 – 162
Solution:
(x2 + 9) (2x 6)
=
2(x 4 – 81)
(x2 + 9) 2(x – 3 )
= x+3
2( x2 + 9) ( x – 3) ( x + 3)
=
(x2 + 9) 2(x – 3)
11
...
(x2 + 3x + 2) ( x2 + 5x + 6)
= ( x + 1) ( x + 3)
–
(x + 1) (x + 2) (x + 2) (x + 3)
=
=
–
( x + 2) 2
x2 ( x2 + 4x + 3)
Simplify:
x2 (x + 1) (x + 3)
x2
=
x+2
x
( x – 1)( x – 2) ( x2 – 9x + 14)
( x – 7) ( x2 – 3x + 2)
Solution:
x2 – 9x + 14
= (x – 2) (x – 7)
x2 – 3x + 2
= (x – 1) (x – 2)
(x – 1) ( x – 2) (x 2 – 9x + 14)
2
(x – 7) (x – 3x + 2)
(x – 1) (x – 2) (x – 2) (x – 7)
=
(x – 7) (x – 1) (x – 2)
= x–2
Title: Algebra _ Simplification of rational expressions
Description: Algebra _ Simplification of rational expressions Step 1: Factor the numerator and the denominator. Step 2: List restricted values. Step 3: Cancel common factors. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.
Description: Algebra _ Simplification of rational expressions Step 1: Factor the numerator and the denominator. Step 2: List restricted values. Step 3: Cancel common factors. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.