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Title: Algebra _ Multiplication and Division of Rational Expressions
Description: Algebra _ Multiplication and Division of Rational Expressions Multiplying and Dividing Rational Expressions Multiplication of rational expressions works the same way as multiplication of any other fractions. We multi ply the numerators to find the numerator of the product, and then multiply the denominators to find the denominator of the product. Before multiplying, it is helpful to factor the numerators and denominators just as we did when simplifying rational expressions. We are often able to simplify the product of rational expressions.
Description: Algebra _ Multiplication and Division of Rational Expressions Multiplying and Dividing Rational Expressions Multiplication of rational expressions works the same way as multiplication of any other fractions. We multi ply the numerators to find the numerator of the product, and then multiply the denominators to find the denominator of the product. Before multiplying, it is helpful to factor the numerators and denominators just as we did when simplifying rational expressions. We are often able to simplify the product of rational expressions.
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Algebra
Multiplication and Division of Rational Expressions
I
...
11
5mn2
15mn
x
44
Solution:
11
5mn2
2
...
2x + 2y
x
5
x
10
x+y
Solution:
2x + 2y
5
4
...
If P =
x2 + 3
x2 – 1
and Q =
x–1
, find PQ
...
x3 – 8
x2 – 4
x
=
x2 + 3
(x + 1)(x 1)
=
x2 + 3
(x + 1) (2x)
x
x–1
2x
x 2 + 6x + 8
x2 – 2x + 1
Solution:
x3 – 8
x2 – 4
2
x x 2 + 6x + 8
x – 2x + 1
=
=
7
...
x2 – y 2
x
x2 + 2xy + y2
xy + y2
x2 xy
Solution:
x2 – y 2
x2 + 2xy + y2
(x + y) ( x y)
xy + y2
x
=
x2 xy
(x + y)2
9
...
x (x – y)
y
x
=
x4 – 8x
y (x + y)
x
12x + 7x –12 x
9x2 + 6x – 8
x
x
= 1
2
12x – 13x – 4
12x2 – 25x + 12
Solution:
6x2 – x – 2
= 6x2 – 4x + 3x – 2
= 2x (3x 2) + 1 (3x – 2)
8x2 + 6x + 1
= 8x2 + 4x + 2x + 1
= 4x (2x + 1) + 1 (2x + 1)
12x2 – 7x – 12
= (3x + 4) (4x 3)
= 9x2 + 12x – 16x – 8
= 3x (3x + 4) 2 (3x + 4)
12x2 – 13x – 4
= (2x + 1) (4x + 1)
= 12x2 + 16x 9x –12
= 4x (3x + 4) 3 (3x + 4)
9x2 + 6x 8
= (3x – 2) (2x + 1)
= 12x2 – 16x+ 3x – 4
= (3x + 4) (3x 2)
= 4x (3x 4) + 1 (3x 4)
12x2 – 25x + 12
= (3x 4) (4x+ 1)
= 12x2 – 16x – 9x + 12
= (3x 4) (4x )
= 4x (3x 4) 3 (3x 4)
6x2 – x – 2
12x 2+ 7x – 12
x
8x2 + 6x + 1
9x2 + 6x – 8
12x 2 – 13x – 4
x
12x2 – 25x + 12
(3x – 2) (2x + 1) (3x + 4) (4x3) (3x 4) (4x+ 1)
(2x + 1) (4x + 1) (3x + 4) (3x 2) (3x 4) (4x)
= 1
II
...
Solution:
25x2
36y2
14x2
9y2
x
36y2
25x2
56
= 25
75m2
25mn
2
14n
49
2
...
t–2
4s
Solution:
49
25mn
=
21m
2n3
t2 – t – 6
12s2
t–2
4s
x
12 s2
=
t2 – t – 6
=
(t – 2)
12s2
x
4s
(t – 3) (t + 2)
3s (t – 2)
(t – 3) (t + 2)
4
...
x2 – 2xy + y2
x2 – xy
x2 – 5x + 6
x2 – x – 2
=
x+y
(x + y) (x – y)
x
(x– y)2
x (x – y)
1
x
x2 – 6x + 9
x2 – 4x + 4
Solution:
x2 – 6x + 9
x2 – 4x + 4
6
...
If P =
x2 – 36
x2 – 49
and Q =
Solution:
P
Q
x+6
find the value of
x+7
x2 – 36
x2 – 49
=
=
8
...
x+7
x+6
(x – 6) (x + 6)
(x + 7)
x
(x 7) (x + 7)
(x + 6)
x–6
x–7
=
x2 – 5x + 6
x2 – 3x + 2
and B = 2
find the value of A B
...
2 x2 + 5x – 3
2 x2 + 7x + 6
(x 4) (x 5) (x 1) (x 2)
=
x3
x5
2x2 + 5x – 3
2x2 – x – 6
2
Solution: 2 x2 + 5x 3
2 x + 7x + 6
x
2x2 x – 6
2x2 + 5x – 3
2 x2 + 5x 3
-----(1)
= 2x2 + 6x x – 3
= 2x (x + 3) –1 (x + 3) = (x + 3) (2x – 1)
2 x2 + 7x + 6
= 2x2 + 4x + 3x + 6
= 2x (x + 2) + 3 (x + 2) = (x + 2) (2x + 3)
2x2 x – 6
= 2x2 4x + 3x 6
= 2x (x 2) + 3 (x2) = (x 2) (2x + 3)
2
2x + 5x – 3
= 2x2 + 6x – x – 3
= 2x (x + 3) –1 ( x + 3) = (x+ 3) (2x – 1)
(1)
(x+ 3) (2x – 1)
(x – 2) (2x + 3)
x–2
x
=
(x+ 2) (2x + 3)
(x+ 3) (2x – 1)
x+2
10
...
(1)
= 2x2 + 8x x – 4
= 2x (x + 4) – 1 (x + 4) = (x + 4) (2x – 1)
3x2 13x + 4
= 3x2 12x x + 4
= 3x (x – 4) –1 (x 4) = (x – 4) (3x – 1)
6x2 + x– 1
=
6x2 + 3x2x
= 3x (2x + 1) –1 (2x + 1) = (2x + 1)(3x – 1)
4x2 – 1
(1)
= (2x + 1) (2x – 1)
(x + 4)(2x – 1)
(2x + 1)(3x – 1)
x
=
(x – 4)(3x – 1)
(2x + 1)(2x – 1)
x+4
x4
Title: Algebra _ Multiplication and Division of Rational Expressions
Description: Algebra _ Multiplication and Division of Rational Expressions Multiplying and Dividing Rational Expressions Multiplication of rational expressions works the same way as multiplication of any other fractions. We multi ply the numerators to find the numerator of the product, and then multiply the denominators to find the denominator of the product. Before multiplying, it is helpful to factor the numerators and denominators just as we did when simplifying rational expressions. We are often able to simplify the product of rational expressions.
Description: Algebra _ Multiplication and Division of Rational Expressions Multiplying and Dividing Rational Expressions Multiplication of rational expressions works the same way as multiplication of any other fractions. We multi ply the numerators to find the numerator of the product, and then multiply the denominators to find the denominator of the product. Before multiplying, it is helpful to factor the numerators and denominators just as we did when simplifying rational expressions. We are often able to simplify the product of rational expressions.