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Perform the operation and express your answer as a single fraction in simplest form. (5)/(3x^(2))-(4)/(15x^(3)) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline53x2−415x3 \frac{5}{3 x^{2}}-\frac{4}{15 x^{3}} \newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline53x2−415x3 \frac{5}{3 x^{2}}-\frac{4}{15 x^{3}} \newlineAnswer:
  1. Find LCD: To combine the fractions, we need a common denominator. The least common denominator (LCD) for 3x23x^2 and 15x315x^3 is 15x315x^3.
  2. Rewrite first fraction: Rewrite the first fraction with the common denominator by multiplying both the numerator and the denominator by 5x5x. This gives us (5×5x)/(3x2×5x)=25x/15x3(5 \times 5x) / (3x^2 \times 5x) = 25x / 15x^3.
  3. Keep common denominator: The second fraction already has the denominator 15x315x^3, so we do not need to change it. Now we have two fractions with the same denominator: (25x)/(15x3)−(4)/(15x3)(25x)/(15x^3) - (4)/(15x^3).
  4. Subtract numerators: Subtract the numerators and keep the common denominator: (25x−4)/15x3(25x - 4) / 15x^3.
  5. Simplify expression: The numerator cannot be simplified further because 25x25x and 44 do not have any common factors, and the variable xx cannot be canceled with the x3x^3 in the denominator. So, the expression is already in its simplest form.

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