Let's simplify the expression: m/(m-6) + m/7.
Step 1: Identify the denominators: (m-6) and 7.
Step 2: Find the common denominator. Since the denominators are different, we multiply them to get the common denominator: 7(m-6).
Step 3: Rewrite each fraction with the common denominator:
- For m/(m-6), multiply numerator and denominator by 7:
(m × 7) / [(m-6) × 7] = 7m / [7(m-6)] - For m/7, multiply numerator and denominator by (m-6):
(m × (m-6)) / [7 × (m-6)] = m(m-6) / [7(m-6)]
Step 4: Now that the denominators are the same, add the numerators:
7m + m(m-6) over the common denominator 7(m-6)
Step 5: Expand m(m-6):
m × m = m² and m × (-6) = -6m, so m(m-6) = m² - 6m
Step 6: Add the numerators:
7m + m² - 6m = m² + (7m - 6m) = m² + m
Step 7: Write the final simplified expression:
(m² + m) / [7(m - 6)]
Step 8 (Optional): Factor numerator if needed:
m² + m = m(m + 1)
So, the simplified expression is:
m(m + 1) / [7(m - 6)]