Simplify 6/7c-5/9d -1/2c+1/3d

To simplify the expression 6/7c - 5/9d - 1/2c + 1/3d, we can combine like terms.

The terms with variables "c" are 6/7c and -1/2c. To combine them, we need to find a common denominator, which in this case is 14.

Multiplying the first term by 2/2, we get (12/14c). Multiplying the second term by 7/7, we get (-7/14c).

So, the combined terms with "c" become (12/14c - 7/14c).

The terms with variables "d" are -5/9d and 1/3d. To combine them, we need to find a common denominator, which is 9.

Multiplying the first term by 1/1, we get (-5/9d). Multiplying the second term by 3/3, we get (3/9d).

So, the combined terms with "d" become (-5/9d + 3/9d).

Combining the "c" and "d" terms, we have: (12/14c - 7/14c - 5/9d + 3/9d).

Simplifying the coefficients: (6/7 - 1/2 - 5/9 + 1/3)cd.

Finding the common denominator, which is 126: (72/126 - 63/126 - 70/126 + 42/126)cd.

Combining the coefficients: (-21/126)cd.

Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor, which is 21: (-1/6)cd.

Therefore, the simplified expression is (-1/6)cd.