Question: Simplify. \frac{y - 4}{y^2 - 8y + 16}

Solution

To simplify the expression \(\frac{y - 4}{y^2 - 8y + 16}\), follow these steps: First, factor the denominator. Notice that \(y^2 - 8y + 16\) is a perfect square trinomial. It can be rewritten as: \[ y^2 - 8y + 16 = (y - 4)^2 \] Now, the expression can be rewritten as: \[ \frac{y - 4}{(y - 4)^2} \] Since \(y - 4\) is a common factor in both the numerator and the denominator, we can cancel out one \(y - 4\) term: \[ \frac{1}{y - 4} \] The simplified expression is: \[ \frac{1}{y - 4} \]