Questions: Subtract. (7b+2)/(8b)-(b+9)/(2b) Simplify your answer as much as possible.

Transcript text: Subtract. \[ \frac{7 b+2}{8 b}-\frac{b+9}{2 b} \] Simplify your answer as much as possible.

Solution

Solution Steps

To subtract the given fractions, we need to find a common denominator. The denominators are \(8b\) and \(2b\). The least common denominator (LCD) is \(8b\). Once we have the common denominator, we can rewrite each fraction with this denominator, perform the subtraction, and simplify the result.

Step 1: Finding a Common Denominator

To subtract the fractions \(\frac{7b + 2}{8b}\) and \(\frac{b + 9}{2b}\), we first identify the least common denominator (LCD), which is \(8b\).

Step 2: Rewriting the Fractions

We rewrite the second fraction with the common denominator: \[ \frac{b + 9}{2b} = \frac{(b + 9) \cdot 4}{2b \cdot 4} = \frac{4(b + 9)}{8b} = \frac{4b + 36}{8b} \]

Step 3: Performing the Subtraction

Now we can perform the subtraction: \[ \frac{7b + 2}{8b} - \frac{4b + 36}{8b} = \frac{(7b + 2) - (4b + 36)}{8b} = \frac{7b + 2 - 4b - 36}{8b} = \frac{3b - 34}{8b} \]

Step 4: Simplifying the Result

The expression \(\frac{3b - 34}{8b}\) is already in its simplest form.