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

Problem

(3*x)/(x+3)/x/(x2−9)

Solution

1. Rewrite the complex fraction as a multiplication problem by multiplying the numerator by the reciprocal of the denominator.

(3*x)/(x+3)⋅(x2−9)/x

2. Factor the difference of squares in the numerator of the second fraction.

x2−9=(x−3)*(x+3)

3. Substitute the factored form back into the expression.

(3*x)/(x+3)⋅((x−3)*(x+3))/x

4. Cancel the common factors of x and (x+3) from the numerator and the denominator.

(3⋅x)/(x+3)⋅((x−3)*(x+3))/x=3*(x−3)

5. Distribute the constant to find the final simplified form.

3*(x−3)=3*x−9

Final Answer

(3*x)/(x+3)/x/(x2−9)=3*x−9

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