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Simplify. Express your answer as a single fraction in simplest form. \newline2vw+vw4\frac{2}{vw} + \frac{vw}{4}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline2vw+vw4\frac{2}{vw} + \frac{vw}{4}
  1. Identify LCD: 2vw+vw4\frac{2}{vw} + \frac{vw}{4}\newlineIdentify the least common denominator (LCD) for the fractions.\newlineThe LCD for vwvw and 44 is 4vw4vw.
  2. Rewrite fractions: 2vw+vw4\frac{2}{vw} + \frac{vw}{4}\newlineRewrite each fraction with the common denominator 4vw4vw.\newline2vw×44+vw4×vwvw\frac{2}{vw} \times \frac{4}{4} + \frac{vw}{4} \times \frac{vw}{vw}\newline=2×4vw×4+vw×vw4×vw=\frac{2\times 4}{vw\times 4} + \frac{vw\times vw}{4\times vw}\newline=84vw+vw24vw=\frac{8}{4vw} + \frac{vw^2}{4vw}
  3. Combine fractions: 84vw\frac{8}{4vw} + vw24vw\frac{vw^2}{4vw}\newlineCombine the fractions over the common denominator.\newline=8+vw24vw\frac{8 + vw^2}{4vw}
  4. Simplify numerator: 8+vw28 + vw^2\newlineSimplify the numerator if possible.\newlineThe numerator cannot be simplified further as 88 and vw2vw^2 are not like terms.
  5. Simplify denominator: 8+vw28 + vw^2\newlineSimplify the denominator if possible.\newlineThe denominator 4vw4vw is already in simplest form.

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