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Simplify. Write your answer using whole numbers and variables.\newlinen2−5nn−5\frac{n^2 - 5n}{n - 5}

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Full solution

Q. Simplify. Write your answer using whole numbers and variables.\newlinen2−5nn−5\frac{n^2 - 5n}{n - 5}
  1. Identify expression: Identify the expression to simplify.\newlineWe have the expression (n2−5n)/(n−5)(n^2 - 5n)/(n - 5). We need to simplify this expression by factoring if possible.
  2. Factor numerator: Factor the numerator.\newlineThe numerator is n2−5nn^2 - 5n, which can be factored by taking out the common factor nn.\newlinen2−5n=n(n−5)n^2 - 5n = n(n - 5)
  3. Rewrite with factored numerator: Rewrite the expression with the factored numerator.\newlineNow, we can rewrite the original expression as:\newlinen(n−5)n−5\frac{n(n - 5)}{n - 5}
  4. Cancel common factors: Cancel out the common factors.\newlineWe see that (n−5)(n - 5) is a common factor in both the numerator and the denominator. We can cancel this factor out, as long as nn is not equal to 55 (since division by zero is undefined).\newlinen(n−5)n−5=n\frac{n(n - 5)}{n - 5} = n, for n≠5n \neq 5

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