Simplify (2x^2-9x+4)/(12+x-x^2)

Problem

(2*x2−9*x+4)/(12+x−x2)

Solution

1. Factor the numerator by looking for two numbers that multiply to 2⋅4=8 and add to −9 These numbers are −8 and −1

2*x2−8*x−x+4=2*x*(x−4)−1*(x−4)=(2*x−1)*(x−4)

2. Rearrange the denominator into standard form to make factoring easier.

−x2+x+12

3. Factor out a negative one from the denominator.

−(x2−x−12)

4. Factor the quadratic in the denominator by finding two numbers that multiply to −12 and add to −1 These numbers are −4 and 3

−(x−4)*(x+3)

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

((2*x−1)*(x−4))/(−(x−4)*(x+3))

6. Cancel the common factor (x−4) from the numerator and the denominator, noting that x≠4

(2*x−1)/(−(x+3))

7. Distribute the negative sign in the denominator to simplify the final form.

(2*x−1)/(−x−3)

Final Answer

(2*x2−9*x+4)/(12+x−x2)=(1−2*x)/(x+3)

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