Simplify (x^2)/(x^2-4)-(x+1)/(x+2)

Problem

(x2)/(x2−4)−(x+1)/(x+2)

Solution

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

(x2)/((x−2)*(x+2))−(x+1)/(x+2)

2. Find a common denominator by multiplying the numerator and denominator of the second fraction by (x−2)

(x2)/((x−2)*(x+2))−((x+1)*(x−2))/((x−2)*(x+2))

3. Expand the numerator of the second fraction using the FOIL method.

(x+1)*(x−2)=x2−2*x+x−2

x2−x−2

4. Subtract the numerators over the common denominator, being careful to distribute the negative sign to all terms in the second numerator.

(x2−(x2−x−2))/((x−2)*(x+2))

5. Simplify the numerator by combining like terms.

x2−x2+x+2

x+2

6. Reduce the fraction by canceling the common factor (x+2) from the numerator and the denominator.

(x+2)/((x−2)*(x+2))

1/(x−2)

Final Answer

(x2)/(x2−4)−(x+1)/(x+2)=1/(x−2)

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