To simplify the expression [tex]\(\frac{6-5x}{-3x}\)[/tex], follow these steps:
1. Distribute the denominator: Notice that both terms in the numerator can be divided by the common denominator.
[tex]\[
\frac{6-5x}{-3x} = \frac{6}{-3x} - \frac{5x}{-3x}
\][/tex]
2. Simplify each fraction separately:
- For the first fraction [tex]\(\frac{6}{-3x}\)[/tex]:
[tex]\[
\frac{6}{-3x} = \frac{6}{-3} \cdot \frac{1}{x} = -2 \cdot \frac{1}{x} = -\frac{2}{x}
\][/tex]
- For the second fraction [tex]\(\frac{5x}{-3x}\)[/tex]:
[tex]\[
\frac{5x}{-3x} = \frac{5}{-3} \cdot \frac{x}{x} = -\frac{5}{3} \cdot 1 = -\frac{5}{3}
\][/tex]
3. Combine the simplified terms:
[tex]\[
\frac{6-5x}{-3x} = -\frac{2}{x} - \frac{5}{3}
\][/tex]
4. Rearrange the terms to match a more conventional format (if required). Instead of leaving a negative sign for each term, we can combine them into a single expression:
[tex]\[
\frac{6-5x}{-3x} = -\left(\frac{2}{x} + \frac{5}{3}\right)
\][/tex]
This can also be written as:
[tex]\[
\frac{6-5x}{-3x} = \frac{5}{3} - \frac{2}{x}
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
\frac{6-5x}{-3x} = \frac{5}{3} - \frac{2}{x}
\][/tex]
