Of course! Let's find the numerator for the rational expression given:
[tex]\[
\frac{p}{q}+\frac{6}{q}=\frac{?}{q}
\][/tex]
Here's the step-by-step solution:
1. Identify the common denominator:
Both terms [tex]\(\frac{p}{q}\)[/tex] and [tex]\(\frac{6}{q}\)[/tex] have the same denominator [tex]\(q\)[/tex].
2. Combine the fractions:
Since the denominators are the same, we can simply add the numerators directly.
To combine [tex]\(\frac{p}{q}\)[/tex] and [tex]\(\frac{6}{q}\)[/tex], we keep the common denominator [tex]\(q\)[/tex] and add the numerators:
[tex]\[
\frac{p}{q} + \frac{6}{q} = \frac{p + 6}{q}
\][/tex]
3. Determine the numerator:
The numerator of the resulting expression is the sum of the numerators of the original expressions. So, we add:
[tex]\[
p + 6
\][/tex]
Therefore, the numerator for the expression
[tex]\[
\frac{p}{q}+\frac{6}{q}=\frac{p+6}{q}
\][/tex]
is [tex]\(\boldsymbol{p + 6}\)[/tex].
