Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

First, let's combine the terms with "c" and the terms with "d" separately.

For "c" terms: 6/7c - 1/2c
The denominators are 7 and 2. To find the common denominator, we multiply 7 and 2 which is 14. We then adjust the numerators accordingly.
(6/7c)(2/2) - (1/2c)(7/7)
= 12/14c - 7/14c
= (12 - 7)/14c
= 5/14c

For "d" terms: -5/9d + 1/3d
The denominators are 9 and 3. To find the common denominator, we multiply 9 and 3 which is 27. We then adjust the numerators accordingly.
(-5/9d)(3/3) + (1/3d)(9/9)
= -15/27d + 9/27d
= (-15 + 9)/27d
= -6/27d
= -2/9d

Now we can combine the simplified "c" and "d" terms:

5/14c - 2/9d

Therefore, the simplified expression is 5/14c - 2/9d.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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

First, let's combine the terms with 'c'.

The terms 6/7c and -1/2c have the same variable 'c', so we can add them together. To do that, we need to find a common denominator for the fractions, which in this case is 14.

(6/7c) - (1/2c) = (12/14c) - (7/14c) = (12 - 7) / 14c = 5/14c

Next, let's combine the terms with 'd'.

The terms -5/9d and 1/3d have the same variable 'd', so we can add them together. To do that, we need to find a common denominator for the fractions, which in this case is 9.

(-5/9d) + (1/3d) = (-5/9d) + (3/9d) = (-5 + 3) / 9d = -2/9d

Now, we have simplified the expression to:
5/14c - 2/9d

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression (6/7c - 5/9d - 1/2c + 1/3d), we need to combine like terms. Like terms refer to terms that have the same variable(s) raised to the same power(s).

Let's break down the expression into two parts - one for the terms with 'c' and another for the terms with 'd'.

For the terms with 'c':
(6/7c - 1/2c) can be rewritten as [(12/14c) - (7/14c)] or (12/14c - 7/14c). Since the denominators are the same, we can combine the numerators, resulting in (12 - 7)/14c, which simplifies to (5/14c).

For the terms with 'd':
(-5/9d + 1/3d) can be rewritten as [(-15/27d) + (9/27d)] or (-15/27d + 9/27d). Again, since the denominators are the same, we can combine the numerators, giving us (-15 + 9)/27d, which simplifies to (-6/27d).

Now, let's put the simplified expressions for 'c' and 'd' together:
(5/14c - 6/27d).

So, the simplified expression is (5/14c - 6/27d).