Question

subtract.
\\(\frac{6}{5x} - \frac{3}{2}\\)

select the correct choice below and fill in any answer boxes within your choice.
(simplify your answer. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)
\\(\bigcirc\\) a. \\(\frac{6}{5x} - \frac{3}{2} = \square, x \
eq \square\\)
\\(\bigcirc\\) b. \\(\frac{6}{5x} - \frac{3}{2} = \square\\), no numbers must be excluded.

Explanation:

Step1: Find common denominator

The common denominator of $5x$ and $2$ is $10x$.

Step2: Rewrite fractions with common denominator

$\frac{6}{5x} = \frac{6\times2}{5x\times2} = \frac{12}{10x}$, $\frac{3}{2} = \frac{3\times5x}{2\times5x} = \frac{15x}{10x}$

Step3: Subtract the fractions

$\frac{12}{10x} - \frac{15x}{10x} = \frac{12 - 15x}{10x}$

Step4: Identify excluded value

The original expression has a denominator $5x$, so $5x
eq0 \implies x
eq0$.

Answer:

A. $\frac{6}{5x} - \frac{3}{2} = \frac{12 - 15x}{10x}$, $x
eq0$