Question

Subtract x3x+7−x9x+21 (1 point) Responses 0 0 4x9x+27 the fraction with numerator 4 x and denominator 9 x plus 27 x3x+7 the fraction with numerator x and denominator 3 x plus 7 2x9x+21

Answer 1

To subtract the two fractions \( \frac{x}{3x+7} - \frac{x}{9x+21} \), we first find a common denominator.

The denominators are \(3x + 7\) and \(9x + 21\). Notice that \(9x + 21\) can be factored:

\[
9x + 21 = 9(x + \frac{21}{9}) = 9(x + \frac{7}{3}) = 3(3x + 7)
\]

So, we can rewrite \(9x + 21\) as \(3(3x + 7)\).

Now, the least common denominator (LCD) will be \(3(3x + 7)\).

Next, we rewrite the fractions with the common denominator:

1. For \( \frac{x}{3x+7} \):
\[
\frac{x}{3x+7} = \frac{x \cdot 3}{(3x + 7) \cdot 3} = \frac{3x}{3(3x + 7)}
\]

2. For \( \frac{x}{9x+21} \):
\[
\frac{x}{9x+21} = \frac{x}{3(3x + 7)}
\]

Now we can subtract the two fractions:

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

Thus, the result of the subtraction is

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

This form matches the options provided, specifically the option with \(2x\) and the shared denominator.