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Simplify. Express your answer as a single fraction in simplest form. \newlinex2w\frac{x}{2} - w

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Q. Simplify. Express your answer as a single fraction in simplest form. \newlinex2w\frac{x}{2} - w
  1. Identify Expression: Identify the expression to be simplified.\newlineWe have the expression x2w\frac{x}{2} - w. To combine these terms into a single fraction, we need to have a common denominator.
  2. Find Common Denominator: Find a common denominator.\newlineThe first term already has a denominator of 22, and the second term, ww, can be thought of as w/1w/1. To combine these, we can rewrite ww with a denominator of 22.\newlinew=(w×2)/(1×2)=2w/2w = (w \times 2)/(1 \times 2) = 2w/2
  3. Rewrite with Common Denominator: Rewrite the expression with the common denominator.\newlineNow we rewrite the original expression using our common denominator of 22.\newlinex2w=x22w2\frac{x}{2} - w = \frac{x}{2} - \frac{2w}{2}
  4. Combine Over Common Denominator: Combine the terms over the common denominator.\newlineSince both terms now have the same denominator, we can combine them into a single fraction.\newline(x2w)/2(x - 2w)/2
  5. Check for Further Simplification: Check if the fraction can be simplified further. The numerator x2wx - 2w does not have any common factors with the denominator 22, so the fraction is already in its simplest form.

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