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

Problem

5/(2*x−3)−3/((2*x−3)2)

Solution

1. Identify the least common denominator (LCD) 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 LCD.

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

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

(10*x−15)/((2*x−3)2)−3/((2*x−3)2)

4. Combine the numerators over the common denominator.

(10*x−15−3)/((2*x−3)2)

5. Simplify the numerator by combining like terms.

(10*x−18)/((2*x−3)2)

6. Factor the numerator to see if any further simplification is possible.

(2*(5*x−9))/((2*x−3)2)

Final Answer

5/(2*x−3)−3/((2*x−3)2)=(10*x−18)/((2*x−3)2)

Want more problems? Check here!