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Perform the operation and express your answer as a single fraction in simplest form. 5x+(1)/(4x^(2)) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline5x+14x2 5 x+\frac{1}{4 x^{2}} \newlineAnswer:

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Algebra 2right chevron icon
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.\newline5x+14x2 5 x+\frac{1}{4 x^{2}} \newlineAnswer:
  1. Convert 5x5x to Fraction: To simplify the expression 5x+14x25x + \frac{1}{4x^{2}}, we need to combine the terms into a single fraction. Since 5x5x is not a fraction, we can write it as a fraction with a denominator of 11 to combine it with the second term.
  2. Find Common Denominator: Rewrite 5x5x with a denominator of 11: 5x=5x15x = \frac{5x}{1}.\newlineNow we have two fractions: 5x1+14x2\frac{5x}{1} + \frac{1}{4x^{2}}.
  3. Convert Fractions to LCD: To add these fractions, we need a common denominator. The least common denominator (LCD) for 11 and 4x24x^2 is 4x24x^2.
  4. Add Fractions: We will now convert the first fraction to have the common denominator of 4x24x^2 by multiplying both the numerator and the denominator by 4x24x^2.5x1×4x24x2=20x34x2\frac{5x}{1} \times \frac{4x^2}{4x^2} = \frac{20x^3}{4x^2}.
  5. Simplify Final Expression: Now that both fractions have the same denominator, we can add them together.\newline(20x3)/(4x2)+(1)/(4x2)=(20x3+1)/(4x2)(20x^3)/(4x^2) + (1)/(4x^2) = (20x^3 + 1)/(4x^2).
  6. Simplify Final Expression: Now that both fractions have the same denominator, we can add them together. \newline(20x3)/(4x2)+(1)/(4x2)=(20x3+1)/(4x2)(20x^3)/(4x^2) + (1)/(4x^2) = (20x^3 + 1)/(4x^2).The expression (20x3+1)/(4x2)(20x^3 + 1)/(4x^2) is already in its simplest form because the numerator and the denominator have no common factors other than 11.

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