Subtract. \[ \frac{c-4 d}{7 c}-\frac{8 c-10 d}{7 c} \] Simplify your answer as much as possible.
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Bonus Knowledge
To simplify the expression \[ \frac{c-4 d}{7 c}-\frac{8 c-10 d}{7 c} \] we start by combining the fractions since they have a common denominator. We can write it as follows: \[ \frac{(c-4d) - (8c-10d)}{7c} \] Now we simplify the numerator: \[ (c - 4d) - (8c - 10d) = c - 4d - 8c + 10d = c - 8c - 4d + 10d = -7c + 6d \] Thus, we have: \[ \frac{-7c + 6d}{7c} \] Now, we can separate the terms in the numerator: \[ \frac{-7c}{7c} + \frac{6d}{7c} \] This simplifies to: \[ -1 + \frac{6d}{7c} \] Therefore, the simplified expression is: \[ \boxed{-1 + \frac{6d}{7c}} \]
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