Multiplying Rational Equations

Just like with numerical ratios, products of rational expressions are found by multiplying the numerators together and the denominators together seperately. When multiplying rational expressions, divide out common factors to simplify the product.

Example 1:8x3y4xy2×7x3y22xy3

 8xxxy7xxxyy4xyy2xyyyMultiply straight across and expand the factors of the numerator and denominator.

8xxxy7xxxyy 4xyy2xyyy Simplify by eliminating factors that are in both the numerator and denominator.

7 x 4 y 2 Rewrite the simplified form.


Example 2: 3 x 2 9x x 2 4x5 × x 2 4x5 6x

3x( x3 )×( x5 )( x+1 ) ( x5 )( x+1 )×23x    Multiply and factor the numerator and denominator.

3x( x-3 )×( x-5 )( x+1 ) ( x5 )( x+1 )×23x Eliminate factors that are in both the numerator and denominator.

x-3 2   Rewrite.


Example 3: 4x+20 2x+2 × x 2 +x 4 x 2 +20x

4( x+5 )×x( x+1 ) 2( x+1 )×4x( x+5 ) Multiply and factor the numerator and denominator.

4 ( x + 5 ) × x ( x + 1 ) 2 ( x + 1 ) × 4 x ( x + 5 ) Eliminate factors that are in both the numerator and denominator.

1 2 Rewrite.


Note: When dividing rational expressions, simply use the reciprocal of the rational divisor and the operation becomes multiplication.

Example 4: 5 x 2 y 3x y 3 ÷ 35 x 2 y 42x y 2

5 x 2 y 3x y 3 × 42x y 2 35 x 2 y Rewrite as a multiplication expression by using the reciprocal of the divisor.

5xxy 3xyyy 237xyy 57xxy Expand the factors of the numerator and denominator.

5xxy 3xyyy 237xyy 57xxy Eliminate factors that are in both the numerator and denominator.

2 y Rewrite.


Example 5: x 2 +12x+32 4x+28 ÷ x 2 +4x x 2 49

x 2 +12x+32 4x+28 × x 2 49 x 2 +4x Rewrite as a mutiplication expression.

( x+4 )( x+8 ) 4( x+7 ) × ( x7 )( x+7 ) x( x+4 ) Factor the numerator and denominator.

( x+4 )( x+8 ) 4( x+7 ) ( x-7 )( x+7 ) x( x+4 ) Eliminate factors that are in both the numerator and denominator.

( x+8 )( x+7 ) 4x Rewrite.


Example 6: x 2 3x10 x 2 +4x+3 ÷( x 2 +x2 )

x 2 x6 x 2 2x3 × 1 x 2 +x2 Rewrite as a multiplication expression.

( x3 )( x+2 ) ( x+1 )( x3 ) × 1 ( x+2 )( x1 )    Factor the numerator and denominator.

( x-3 )( x+2 ) ( x+1 )( x-3 ) 1 ( x+2 )( x1 ) Eliminate factors that are in both the numerator and denominator.

1 ( x+1 )( x1 ) Rewrite.


Now that you can multiply and divide rational expressions you are one step closer to solving rational equations.



Related Links:
Math
algebra
Multiplying Rational Expressions Worksheets
Rational Expressions
Simplifying Rational Expressions
Adding Rational Expressions
Algebra Topics


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