To reduce the fraction [tex]\(\frac{k+7}{4k+28}\)[/tex] to its lowest terms, we can follow these steps:
1. Identify and Factor the Numerator and Denominator:
- Numerator: [tex]\( k + 7 \)[/tex]
- Denominator: [tex]\( 4k + 28 \)[/tex]
Notice that [tex]\(4k + 28\)[/tex] has a common factor in both terms.
2. Factor the Denominator:
- [tex]\(4k + 28\)[/tex] can be factored as [tex]\(4(k + 7)\)[/tex].
3. Rewrite the Fraction:
- [tex]\[
\frac{k+7}{4(k+7)}
\][/tex]
4. Cancel the Common Factor:
- The common factor [tex]\(k + 7\)[/tex] in the numerator and the denominator can be canceled out, provided that [tex]\(k \neq -7\)[/tex] (because if [tex]\(k = -7\)[/tex], both the original numerator and denominator would be zero, which is undefined). This leaves us with:
[tex]\[
\frac{1}{4}
\][/tex]
Thus, the fraction [tex]\(\frac{k+7}{4k+28}\)[/tex], when reduced to its lowest terms, is:
[tex]\[
\frac{1}{4}
\][/tex]
