Question

subtract.
\\(\frac{6b - 5}{8b} - \frac{3b - 4}{6b}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find the least common denominator (LCD) of the two fractions. The denominators are \(8b\) and \(6b\). The prime factors of 8 are \(2^3\) and of 6 are \(2\times3\), so the LCD of 8 and 6 is \(2^3\times3 = 24\), and including \(b\), the LCD is \(24b\).

Step2: Rewrite each fraction with the LCD. For \(\frac{6b - 5}{8b}\), multiply numerator and denominator by 3: \(\frac{(6b - 5)\times3}{8b\times3}=\frac{18b - 15}{24b}\). For \(\frac{3b - 4}{6b}\), multiply numerator and denominator by 4: \(\frac{(3b - 4)\times4}{6b\times4}=\frac{12b - 16}{24b}\).

Step3: Subtract the two fractions: \(\frac{18b - 15}{24b}-\frac{12b - 16}{24b}=\frac{(18b - 15)-(12b - 16)}{24b}\).

Step4: Simplify the numerator: \(18b - 15 - 12b + 16=(18b - 12b)+(-15 + 16)=6b + 1\).

Step5: The resulting fraction is \(\frac{6b + 1}{24b}\).

Answer:

\(\frac{6b + 1}{24b}\)