Question
Subtract. \[ \frac{c-4 d}{7 c}-\frac{8 c-10 d}{7 c} \] Simplify your answer as much as possible.
Ask by Simmons Moreno. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{-7c + 6d}{7c}\)
Solution
Calculate or simplify the expression \( \frac{c-4d}{7c}-\frac{8c-10d}{7c} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{c-4d}{7c}-\frac{8c-10d}{7c}\)
- step1: Transform the expression:
\(\frac{c-4d-\left(8c-10d\right)}{7c}\)
- step2: Subtract the terms:
\(\frac{-7c+6d}{7c}\)
The result of subtracting \(\frac{c-4d}{7c}\) from \(\frac{8c-10d}{7c}\) is \(\frac{-7c+6d}{7c}\).
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Simplify this solution 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: \[ \boxed{-1 + \frac{6d}{7c}} \]
