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Simplify. Write your answer using whole numbers and variables.\newline4n2−9n4n−9\frac{4n^2 - 9n}{4n - 9}

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Full solution

Q. Simplify. Write your answer using whole numbers and variables.\newline4n2−9n4n−9\frac{4n^2 - 9n}{4n - 9}
  1. Identify Expression: Identify the expression to be simplified.\newlineThe expression given is a rational expression (a fraction) where the numerator is 4n2−9n4n^2 - 9n and the denominator is 4n−94n - 9.
  2. Factor Numerator: Factor the numerator if possible.\newlineWe look for common factors in the terms of the numerator. The terms 4n24n^2 and −9n-9n have a common factor of nn.\newline4n2−9n=n(4n−9)4n^2 - 9n = n(4n - 9)
  3. Cancel Common Factors: Simplify the expression by canceling out common factors.\newlineThe numerator is now n(4n−9)n(4n - 9), and the denominator is 4n−94n - 9. We can see that the factor (4n−9)(4n - 9) is common to both the numerator and the denominator, so we can cancel it out.\newlinen(4n−9)4n−9=n\frac{n(4n - 9)}{4n - 9} = n
  4. Write Final Expression: Write the final simplified expression.\newlineAfter canceling out the common factor, we are left with nn as the simplified expression.

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