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Simplify. Express your answer as a single fraction in simplest form. \newlinew42+2wx\frac{w^4}{2} + \frac{2}{wx}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinew42+2wx\frac{w^4}{2} + \frac{2}{wx}
  1. Identify LCM: Identify the least common multiple (LCM) of the denominators 22 and wxwx. Since 22 and wxwx have no common factors other than 11, the LCM is simply 2wx2wx.
  2. Make denominators same: Make the denominators the same by multiplying the first fraction by wxwx\frac{wx}{wx} and the second fraction by 22\frac{2}{2}. This gives us w4⋅wx2⋅wx+2⋅2wx⋅2\frac{w^4 \cdot wx}{2 \cdot wx} + \frac{2 \cdot 2}{wx \cdot 2}.
  3. Perform multiplications: Perform the multiplications in the numerators and denominators. This results in (w5x)/(2wx)+(4)/(2wx)(w^5x)/(2wx) + (4)/(2wx).
  4. Combine fractions: Combine the fractions since the denominators are now the same. The combined fraction is (w5x+4)/(2wx)(w^5x + 4)/(2wx).
  5. Check for simplification: Check if the expression can be simplified further. Since w5xw^5x and 44 have no common factors, the fraction is already in its simplest form.

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