Simplify the rational expression
2x^3-x^2-6x ➗2x^2-7x+6
Pls show steps I want to understand thank u!
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I don't know what the ➗ is supposed to be.
To simplify the rational expression (2x^3 - x^2 - 6x) ÷ (2x^2 - 7x + 6), follow these steps:
Step 1: Factor both the numerator and the denominator.
The numerator: 2x^3 - x^2 - 6x
Factor out the greatest common factor (GCF) which is x: x(2x^2 - x - 6)
Further factor the quadratic expression: x(2x + 3)(x - 2)
The denominator: 2x^2 - 7x + 6
Factor the quadratic expression: (2x - 3)(x - 2)
Step 2: Write the rational expression as a multiplication of the reciprocal of the denominator.
The rational expression becomes: [x(2x + 3)(x - 2)] / [(2x - 3)(x - 2)]
Step 3: Cancel out common factors.
In the numerator, we have (x - 2) in both the denominator and the numerator, so we can cancel it out.
The expression simplifies to: x(2x + 3) / (2x - 3)
Therefore, the simplified form of the rational expression (2x^3 - x^2 - 6x) ÷ (2x^2 - 7x + 6) is x(2x + 3) / (2x - 3).
Note: Remember, factoring and canceling common factors are crucial steps in simplifying rational expressions.