Question

evaluate the expression when a = 30 and b = 6.\\(dfrac{a + b^2}{a - 4b}\\)simplify your answer as much as possible.

Explanation:

Step1: Substitute \(a = 30\) and \(b = 6\) into the expression.

First, calculate \(b^{2}\), \(a + b^{2}\), and \(a - 4b\) separately.
For \(b^{2}\), when \(b = 6\), \(b^{2}=6^{2}=36\).
For \(a + b^{2}\), when \(a = 30\) and \(b^{2}=36\), \(a + b^{2}=30 + 36 = 66\).
For \(a - 4b\), when \(a = 30\) and \(b = 6\), \(a - 4b=30-4\times6 = 30 - 24 = 6\).

Step2: Substitute the calculated values into the original fraction.

The original expression \(\frac{a + b^{2}}{a - 4b}\) becomes \(\frac{66}{6}\).

Step3: Simplify the fraction.

\(\frac{66}{6}=11\).

Answer:

\(11\)