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Simplify. Express your answer as a single fraction in simplest form. \newlinev+v+ w25\frac{w^2}{5}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newlinev+v+ w25\frac{w^2}{5}
  1. Identify Terms: Identify the terms in the expression that need to be combined into a single fraction.\newlineThe expression is v+w25v + \frac{w^2}{5}. To combine these into a single fraction, we need to have a common denominator.
  2. Find Common Denominator: Find a common denominator for the terms.\newlineSince vv is not a fraction, we can think of it as v/1v/1. The common denominator for 11 and 55 is 55.
  3. Convert to Fraction: Convert vv to a fraction with the common denominator.\newlineTo convert vv to a fraction with a denominator of 55, we multiply both the numerator and the denominator by 55: (v×5)/(1×5)=5v5.(v \times 5)/(1 \times 5) = \frac{5v}{5}.
  4. Rewrite Expression: Rewrite the expression with the common denominator.\newlineNow we have 5v5+w25\frac{5v}{5} + \frac{w^2}{5}.
  5. Combine Fractions: Combine the fractions over the common denominator.\newlineSince both fractions now have the same denominator, we can combine the numerators: (5v+w2)/5(5v + w^2)/5.
  6. Check for Simplification: Check if the fraction can be simplified further.\newlineThe fraction (5v+w2)/5(5v + w^2)/5 is already in simplest form because the numerator and the denominator do not have any common factors other than 11.

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