Sure! Let's go through the steps to find the difference and express the answer in simplest form.
1. Identify the given expression:
[tex]\[
\frac{6x}{y} - \frac{x}{y}
\][/tex]
2. Combine the fractions:
Since both fractions have the same denominator [tex]\( y \)[/tex], we can combine the numerators:
[tex]\[
\frac{6x}{y} - \frac{x}{y} = \frac{6x - x}{y}
\][/tex]
3. Simplify the numerator:
Simplify the numerator by subtracting [tex]\( x \)[/tex] from [tex]\( 6x \)[/tex]:
[tex]\[
6x - x = 5x
\][/tex]
4. Write the simplified expression:
Now, place the simplified numerator back over the denominator [tex]\( y \)[/tex]:
[tex]\[
\frac{5x}{y}
\][/tex]
So, the difference [tex]\(\frac{6x}{y} - \frac{x}{y}\)[/tex] expressed in its simplest form is:
[tex]\[
\frac{5x}{y}
\][/tex]
