Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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]
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]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.