Simplify (2x^2+3x-2)/(x^2-9)

Problem

(2*x2+3*x−2)/(x2−9)

Solution

1. Factor the numerator by finding two numbers that multiply to 2⋅(−2)=−4 and add to 3 These numbers are 4 and −1

2*x2+4*x−x−2

2*x*(x+2)−1*(x+2)

(2*x−1)*(x+2)

2. Factor the denominator using the difference of squares formula a2−b2=(a−b)*(a+b)

x2−3

(x−3)*(x+3)

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

((2*x−1)*(x+2))/((x−3)*(x+3))

4. Check for common factors in the numerator and denominator to simplify further. Since there are no common factors, the expression is already in its simplest form.

Final Answer

(2*x2+3*x−2)/(x2−9)=((2*x−1)*(x+2))/((x−3)*(x+3))

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