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Perform the operation and express your answer as a single fraction in simplest form. (5x)/(2)+(1)/(3x^(2)) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline5x2+13x2 \frac{5 x}{2}+\frac{1}{3 x^{2}} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline5x2+13x2 \frac{5 x}{2}+\frac{1}{3 x^{2}} \newlineAnswer:
  1. Find LCD: To add the two fractions, we need a common denominator. The least common denominator (LCD) for 22 and 3x23x^2 is 6x26x^2.
  2. First Fraction: Multiply the numerator and denominator of the first fraction by 3x23x^2 to get the common denominator.\newline($5x2(\$\frac{5x}{2}) * (3x23x2\frac{3x^2}{3x^2}) = 15x36x2\frac{15x^3}{6x^2})
  3. Second Fraction: Multiply the numerator and denominator of the second fraction by 22 to get the common denominator.\newline($13x2(\$\frac{1}{3}x^2) * (22\frac{2}{2}) = (26x2\frac{2}{6}x^2)
  4. Add Numerators: Now that we have a common denominator, we can add the numerators. \newline(15x36x2)+(26x2)=15x3+26x2(\frac{15x^3}{6x^2}) + (\frac{2}{6x^2}) = \frac{15x^3 + 2}{6x^2}
  5. Simplify Expression: The expression is already simplified, and there are no common factors to cancel out in the numerator and denominator.

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