Rational Expressions Multiplier
Expression 1
x +
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x +
Expression 2
x +
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x +
Resulting Product (Expanded Form):
Understanding Rational Expressions
A rational expression is essentially a fraction where both the numerator and the denominator are polynomials. In algebra, working with these expressions is similar to working with numerical fractions, but you must account for variables and polynomial arithmetic.
How to Multiply Rational Expressions
Multiplying two rational expressions is straightforward: you multiply the numerators together and the denominators together. The rule is:
(P/Q) * (R/S) = (P * R) / (Q * S)
For linear terms like (ax + b), the multiplication follows the FOIL method (First, Outer, Inner, Last), resulting in a quadratic expression (Ax² + Bx + C).
The Importance of the Domain
The domain of a rational expression includes all real numbers except those that make the denominator equal to zero. Dividing by zero is undefined in mathematics. When you multiply two expressions, the new domain excludes any values that would have made either of the original denominators zero.
Example Calculation
If you multiply (x + 2) / (x + 3) by (x + 4) / (x + 5):
- Numerator: (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8
- Denominator: (x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15
- Result: (x² + 6x + 8) / (x² + 8x + 15)
- Excluded Values: x cannot be -3 or -5.