Question

x over 3x+7 minus x over 9x+21

Answer 1

Why must i give you choices every time I really think you dont know
4x over 9x+27
x over 3x+7
2x over 9x+21
0

Answer 2

To simplify the expression \(\frac{x}{3x + 7} - \frac{x}{9x + 21}\), we first notice that the second denominator can be factored. Specifically, we can rewrite \(9x + 21\) as \(9(x + \frac{21}{9}) = 9(x + \frac{7}{3})\), but for simplification, let us factor it differently:

\[
9x + 21 = 9(x + \frac{21}{9}) = 9(x + 2\frac{1}{3}) = 9(x + 2.333...)
\]

However, it's simpler to identify common factors: \(9x + 21 = 3(3x + 7)\).

Now, we can rewrite the expression:

\[
\frac{x}{3x + 7} - \frac{x}{3(3x + 7)}
\]

To combine these fractions, we get a common denominator. The common denominator is \(3(3x + 7)\):

1. Rewrite the first fraction:
\[
\frac{x}{3x + 7} = \frac{x \cdot 3}{3(3x + 7)} = \frac{3x}{3(3x + 7)}
\]

With this, we have:

\[
\frac{3x}{3(3x + 7)} - \frac{x}{3(3x + 7)} = \frac{3x - x}{3(3x + 7)}
\]

2. Combine the numerators:
\[
3x - x = 2x
\]

So the expression becomes:

\[
\frac{2x}{3(3x + 7)}
\]

This is the simplified form of the original expression. Therefore, the final result is:

\[
\frac{2x}{3(3x + 7)}
\]

Answer 3

Let’s evaluate the original expression you provided again:

\[
\frac{x}{3x + 7} - \frac{x}{9x + 21}
\]

We need to check if this expression simplifies to any of the choices you provided.

1. Note that \(9x + 21\) can be factored out as \(3(3x + 7)\), so the expression can be rewritten as:

\[
\frac{x}{3x + 7} - \frac{x}{3(3x + 7)}
\]

2. Now, use a common denominator to combine the fractions. The common denominator is \(3(3x + 7)\):

\[
\frac{x}{3x + 7} = \frac{x \cdot 3}{3(3x + 7)} = \frac{3x}{3(3x + 7)}
\]

So now, we rewrite the expression:

\[
\frac{3x}{3(3x + 7)} - \frac{x}{3(3x + 7)} = \frac{3x - x}{3(3x + 7)} = \frac{2x}{3(3x + 7)}
\]

Next, we can check if this is equivalent to any of the choices.

Now, let's compare:

1. **Choice 1**: \(\frac{4x}{9x + 27}\)
- Factoring out \(9\) gives: \(\frac{4x}{9(x + 3)}\)

2. **Choice 2**: \(\frac{x}{3x + 7}\)
- This is just \(\frac{x}{3x + 7}\).

3. **Choice 3**: \(\frac{2x}{9x + 21}\)
- Factoring out \(3\) gives: \(\frac{2x}{3(3x + 7)}\), which is exactly the same as our result \(\frac{2x}{3(3x + 7)}\).

4. **Choice 4**: \(0\)

Comparing,

- Our simplified expression is \(\frac{2x}{3(3x + 7)}\), which matches with **Choice 3**: \(\frac{2x}{9x + 21}\).

Thus, the answer is:

**Choice 3: \(\frac{2x}{9x + 21}\)**.