To simplify the expression \(\frac{3b^2 + 33b}{11b}\), we can follow these steps:
-
Factor the Numerator: The numerator is \(3b^2 + 33b\). We can factor out the common term, which is \(3b\): \[ 3b^2 + 33b = 3b(b + 11) \]
-
Rewrite the Expression: Now, substitute the factored form back into the original expression: \[ \frac{3b(b + 11)}{11b} \]
-
Cancel Common Factors: In the expression \(\frac{3b(b + 11)}{11b}\), we can cancel the \(b\) in the numerator and the denominator (assuming \(b \neq 0\)): \[ = \frac{3(b + 11)}{11} \]
This means that the expression simplifies to: \[ \frac{3(b + 11)}{11} \]
- Result: The final simplified form is: \[ \frac{3(b + 11)}{11} \]
This represents the fully simplified version of the original expression, providing a clearer insight into the relationship between the variables.
Summary
To summarize, we factored the numerator, canceled the common terms, and simplified the expression to arrive at the final result.
Remember: Always ensure that the variable \(b\) is not equal to zero when canceling the \(b\) from the numerator and denominator, as division by zero is undefined.