%2F6x%5E2.jpeg "(18x^3+12x^2-3x)/6x^2")
Simplifying the Expression (18x³ + 12x² - 3x) / 6x²
This article will guide you through simplifying the expression (18x³ + 12x² - 3x) / 6x². We'll use the concept of factoring to break down the expression and cancel out common factors.
Understanding the Expression
The expression (18x³ + 12x² - 3x) / 6x² represents a rational expression, which is a fraction where both the numerator and denominator are polynomials.
Simplifying the Expression
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Factor out the Greatest Common Factor (GCF) from the numerator:
The GCF of 18x³, 12x², and -3x is 3x. Factoring out 3x from the numerator gives us:
(18x³ + 12x² - 3x) = 3x (6x² + 4x - 1) -
Rewrite the expression with factored numerator:
The expression now becomes:
(18x³ + 12x² - 3x) / 6x² = [3x (6x² + 4x - 1)] / 6x² -
Cancel out common factors:
Both the numerator and denominator have a common factor of 3x. Canceling these out:
[3x (6x² + 4x - 1)] / 6x² = (6x² + 4x - 1) / 2x
Simplified Expression
Therefore, the simplified form of the expression (18x³ + 12x² - 3x) / 6x² is (6x² + 4x - 1) / 2x.
Note: This simplified expression is valid for all values of x except for x = 0, as this would make the denominator zero, resulting in an undefined expression.