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Simplifying the Expression (12x³y² - 15x²y³)/(-3x²y²)
This article will guide you through the process of simplifying the algebraic expression (12x³y² - 15x²y³)/(-3x²y²).
Understanding the Expression
The expression represents a division of two terms:
- Numerator: 12x³y² - 15x²y³
- Denominator: -3x²y²
Simplifying the Expression
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Factor out the Greatest Common Factor (GCF) from the numerator: The GCF of 12x³y² and 15x²y³ is 3x²y². Therefore, we can rewrite the numerator as:
12x³y² - 15x²y³ = 3x²y²(4x - 5y) -
Rewrite the expression with the factored numerator:
(12x³y² - 15x²y³)/(-3x²y²) = [3x²y²(4x - 5y)] / (-3x²y²) -
Cancel out the common factors: Notice that both the numerator and denominator share the factor 3x²y². We can cancel these out:
[3x²y²(4x - 5y)] / (-3x²y²) = (4x - 5y) / (-1) -
Simplify further: Since dividing by -1 simply changes the sign of the expression:
(4x - 5y) / (-1) = -4x + 5y
Final Result
Therefore, the simplified form of the expression (12x³y² - 15x²y³)/(-3x²y²) is -4x + 5y.