Subtract 2/(15x)-4/(21x^2)

Problem

2/(15*x)−4/(21*x2)

Solution

1. Find the least common denominator (LCD) by determining the least common multiple of the coefficients 15 and 21 and the highest power of x

15=3⋅5

21=3⋅7

LCD=3⋅5⋅7⋅x2=105*x2

2. Rewrite each fraction with the LCD by multiplying the numerator and denominator of each term by the necessary factors.

(2⋅7*x)/(15*x⋅7*x)−(4⋅5)/(21*x2⋅5)

3. Simplify the numerators and denominators.

(14*x)/(105*x2)−20/(105*x2)

4. Subtract the numerators over the common denominator.

(14*x−20)/(105*x2)

5. Factor the numerator to see if the fraction can be simplified further.

(2*(7*x−10))/(105*x2)

Final Answer

2/(15*x)−4/(21*x2)=(14*x−20)/(105*x2)

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