Simplify 7/(2x-3)-5/((2x-3)^2)

Problem

7/(2*x−3)−5/((2*x−3)2)

Solution

1. Identify the least common denominator for the two fractions, which is (2*x−3)2

2. Rewrite the first fraction by multiplying both the numerator and the denominator by (2*x−3) to match the common denominator.

(7*(2*x−3))/((2*x−3)*(2*x−3))−5/((2*x−3)2)

3. Distribute the 7 in the numerator of the first fraction.

(14*x−21)/((2*x−3)2)−5/((2*x−3)2)

4. Combine the numerators over the common denominator.

(14*x−21−5)/((2*x−3)2)

5. Simplify the numerator by combining the constant terms.

(14*x−26)/((2*x−3)2)

Final Answer

7/(2*x−3)−5/((2*x−3)2)=(14*x−26)/((2*x−3)2)

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