Question

Add or subtract, as indicated. See Example 4. (1/6m) + (2/5m) + (4/m)

Accepted Answer

Identify the terms to be added: $$\frac{1}{6m}$$, $$\frac{2}{5m}$$, and $$\frac{4}{m}. $$Since all terms have the variable $$m in $$the denominator, we will treat $$m as a $$common factor in the denominators. Find the least common denominator (LCD) for the fractions. The denominators are $$6m$$, $$5m$$, and $$m. $$The LCD for the numeric parts 6, 5, and 1 is the least common multiple (LCM) of 6 and 5, which is 30. Since all denominators have $$m$$, the LCD is $$30m. $$Rewrite each fraction with the common denominator $$30m by $$multiplying numerator and denominator appropriately: 
- For $$\frac{1}{6m}$$, multiply numerator and denominator by 5 to get $$\frac{5}{30m}.
- $$For $$\frac{2}{5m}$$, multiply numerator and denominator by 6 to get $$\frac{12}{30m}.
- $$For $$\frac{4}{m}$$, multiply numerator and denominator by 30 to get $$\frac{120}{30m}. $$Add the numerators over the common denominator: $$\frac{5}{30m} + \frac{12}{30m} + \frac{120}{30m} = \frac{5 + 12 + 120}{30m}. $$Combine the numerators to get a single fraction: $$\frac{137}{30m}. $$This is the simplified sum of the original expression.

Add or subtract, as indicated. See Example 4. (1/6m) + (2/5m) + (4/m)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Adding and Subtracting Algebraic Fractions

Finding the Least Common Denominator (LCD)

Simplifying Algebraic Expressions