Simplify (2x^3-x^2-6x)/(2x^2-7x+6)

Problem

(2*x3−x2−6*x)/(2*x2−7*x+6)

Solution

1. Factor the numerator by first pulling out the greatest common factor, which is x

2*x3−x2−6*x=x*(2*x2−x−6)

2. Factor the quadratic remaining in the numerator, 2*x2−x−6 into two binomials.

x*(2*x2−x−6)=x*(2*x+3)*(x−2)

3. Factor the denominator quadratic expression 2*x2−7*x+6 into two binomials.

2*x2−7*x+6=(2*x−3)*(x−2)

4. Rewrite the expression using the factored forms of the numerator and the denominator.

(x*(2*x+3)*(x−2))/((2*x−3)*(x−2))

5. Cancel the common factor (x−2) from both the numerator and the denominator, noting that x≠2

(x*(2*x+3))/(2*x−3)

Final Answer

(2*x3−x2−6*x)/(2*x2−7*x+6)=(2*x2+3*x)/(2*x−3)

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