Identify the LCD in the equation below. $$ \frac{2}{x}+\frac{7}{8 x}=\frac{3}{x^{2}} $$ $$ 8 x $$ $$ x $$ $$ 8 x^{2} $$ $$ x^{2} $$

Question

UpStudy AI · Accepted Answer

To find the least common denominator (LCD) in the equation

$$
\frac{2}{x}+\frac{7}{8 x}=\frac{3}{x^{2}},
$$

we need to identify the denominators present in each term:

1. The first term has a denominator of $$ x $$.
2. The second term has a denominator of $$ 8x $$.
3. The third term has a denominator of $$ x^2 $$.

Now, let's break down the denominators:

- $$ x $$ can be expressed as $$ x^1 $$.
- $$ 8x $$ can be expressed as $$ 8 \cdot x^1 $$.
- $$ x^2 $$ is already in its simplest form.

To find the LCD, we take the highest power of each factor present in the denominators:

- The highest power of $$ x $$ is $$ x^2 $$.
- The constant $$ 8 $$ is also present in the second term.

Thus, the LCD is:

$$
8 \cdot x^2.
$$

Therefore, the least common denominator (LCD) for the equation is $$ 8x^2 $$.

The correct answer is:

$$ 8x^2 $$.
The LCD is $$ 8x^2 $$.

Identify the LCD in the equation below. \( \frac{2}{x}+\frac{7}{8 x}=\frac{3}{x^{2}} \) \( 8 x \) \( x \) \( 8 x^{2} \) \( x^{2} \)