Certainly! Let's subtract the given fractions step by step.
Given the expression:
[tex]\[
\frac{a+15}{a} - \frac{b-15}{b}
\][/tex]
We will handle subtracting these fractions. To find a common denominator, we can use \( a \times b \) since the denominators are \( a \) and \( b \) respectively. Let's rewrite each fraction with this common denominator:
[tex]\[
\frac{a+15}{a} = \frac{(a+15) \times b}{a \times b}
\][/tex]
[tex]\[
\frac{b-15}{b} = \frac{(b-15) \times a}{b \times a}
\][/tex]
Now, the expression becomes:
[tex]\[
\frac{(a+15) \times b}{a \times b} - \frac{(b-15) \times a}{a \times b}
\][/tex]
Since both fractions now have the same denominator, we can combine the numerators:
[tex]\[
\frac{(a+15) \times b - (b-15) \times a}{a \times b}
\][/tex]
Distribute the terms in the numerators:
[tex]\[
\frac{ab + 15b - ab + 15a}{a \times b}
\][/tex]
Notice that \( ab \) and \( -ab \) cancel each other out:
[tex]\[
\frac{15b + 15a}{a \times b}
\][/tex]
We can factor out the common term \( 15 \) in the numerator:
[tex]\[
\frac{15(b + a)}{a \times b}
\][/tex]
And thus, the final simplified expression is:
[tex]\[
-(b - 15)/b + (a + 15)/a
\][/tex]
So, the subtraction of the given fractions yields:
[tex]\[
\frac{a+15}{a} - \frac{b-15}{b} = -(b - 15)/b + (a + 15)/a
\][/tex]
