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Perform the operation and express your answer as a single fraction in simplest form. (1)/(2x)+(3)/(4) Answer:

Perform the operation and express your answer as a single fraction in simplest form.\newline12x+34 \frac{1}{2 x}+\frac{3}{4} \newlineAnswer:

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Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.\newline12x+34 \frac{1}{2 x}+\frac{3}{4} \newlineAnswer:
  1. Identify LCD: Identify the Least Common Denominator (LCD) The LCD for the fractions 12x\frac{1}{2x} and 34\frac{3}{4} is 4⋅(2x)4\cdot(2x) because 2x2x and 44 have no common factors other than 11, and thus their LCD is simply their product.
  2. Rewrite with LCD: Rewrite each fraction with the LCD as the new denominator\newlineFor the first fraction, 12x\frac{1}{2x}, we multiply the numerator and denominator by 22 to get 2×12×2x=24x\frac{2\times 1}{2\times 2x} = \frac{2}{4x}.\newlineFor the second fraction, 34\frac{3}{4}, we multiply the numerator and denominator by 2x2x to get 3×2x4×2x=6x4x×2\frac{3\times 2x}{4\times 2x} = \frac{6x}{4x\times 2}.
  3. Combine fractions: Combine the fractions\newlineNow that both fractions have the same denominator, we can combine them into a single fraction.\newline(24x)+(6x4x⋅2)=2+6x4x⋅2(\frac{2}{4x}) + (\frac{6x}{4x\cdot 2}) = \frac{2 + 6x}{4x\cdot 2}
  4. Simplify numerator: Simplify the numerator Simplify the expression in the numerator by combining like terms. 2+6x=6x+22 + 6x = 6x + 2
  5. Write final answer: Write the final answer\newlineThe final answer is (6x+2)/(8x)(6x + 2)/(8x), which is already in simplest form because the numerator and denominator have no common factors other than 11.

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