IDNLearn.com is your trusted platform for finding reliable answers. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
Certainly! Let's work through each of the given expressions step by step and provide the simplified results.
### 1. [tex]\(\frac{2}{a^2 b^3} - \frac{1}{a b}\)[/tex]
First, let's simplify the fraction:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1}{a b} \][/tex]
To combine these fractions, we need a common denominator, which is [tex]\(a^2 b^3\)[/tex]:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1 \cdot a}{a \cdot a b^3} = \frac{2}{a^2 b^3} - \frac{a b^2}{a^2 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{2 - a b^2}{a^2 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1}{a b} = \frac{2 - a b^2}{a^2 b^3} \][/tex]
### 2. [tex]\(\frac{1}{a b^2} - \frac{1}{a^3 b}\)[/tex]
Next, we'll handle the second expression:
[tex]\[ \frac{1}{a b^2} - \frac{1}{a^3 b} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^2\)[/tex]:
[tex]\[ \frac{1 \cdot a^2}{a^2 \cdot a b^2} - \frac{1 \cdot b}{a^3 \cdot b b} = \frac{a^2}{a^3 b^2} - \frac{b}{a^3 b^2} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{a^2 - b}{a^3 b^2} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{a b^2} - \frac{1}{a^3 b} = \frac{a^2 - b}{a^3 b^2} \][/tex]
### 3. [tex]\(\frac{2}{a^3 b^3} - \frac{1}{a^2 b^3}\)[/tex]
Simplify the third expression:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^3\)[/tex]:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1 \cdot a}{a \cdot a^2 b^3} = \frac{2}{a^3 b^3} - \frac{a}{a^3 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{2 - a}{a^3 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} = \frac{2 - a}{a^3 b^3} \][/tex]
### 4. [tex]\(\frac{1}{a^3 b^2} - \frac{1}{a^2 b^3}\)[/tex]
Simplify the fourth expression:
[tex]\[ \frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^3\)[/tex]:
[tex]\[ \frac{1 \cdot b}{a^3 \cdot b b^2} - \frac{1 \cdot a}{a \cdot a^2 b^3} = \frac{b}{a^3 b^3} - \frac{a}{a^3 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{b - a}{a^3 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} = \frac{b - a}{a^3 b^3} \][/tex]
### 5. [tex]\(\frac{a^2 - b}{a^3 b^2}\)[/tex]
This expression is already in its simplified form:
[tex]\[ \frac{a^2 - b}{a^3 b^2} \][/tex]
### 6. [tex]\(\frac{b - a}{a^9 b^9}\)[/tex]
This expression is also already simplified in its simplest form:
[tex]\[ \frac{b - a}{a^9 b^9} \][/tex]
### 7. [tex]\(\frac{2 - a b^2}{a^2 b^3}\)[/tex]
This expression is a straightforward fraction and is already in its simplest form:
[tex]\[ \frac{2 - a b^2}{a^2 b^3} \][/tex]
### 8. [tex]\(\frac{2 - a}{a^3 b^3}\)[/tex]
Finally, this expression is also a simplified fraction:
[tex]\[ \frac{2 - a}{a^3 b^3} \][/tex]
Thus, the final simplified forms for these expressions are:
1. [tex]\(\frac{2}{a^2 b^3} - \frac{1}{a b} = \frac{2 - a b^2}{a^2 b^3}\)[/tex]
2. [tex]\(\frac{1}{a b^2} - \frac{1}{a^3 b} = \frac{a^2 - b}{a^3 b^2}\)[/tex]
3. [tex]\(\frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} = \frac{2 - a}{a^3 b^3}\)[/tex]
4. [tex]\(\frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} = \frac{b - a}{a^3 b^3}\)[/tex]
5. [tex]\(\frac{a^2 - b}{a^3 b^2}\)[/tex]
6. [tex]\(\frac{b - a}{a^9 b^9}\)[/tex]
7. [tex]\(\frac{2 - a b^2}{a^2 b^3}\)[/tex]
8. [tex]\(\frac{2 - a}{a^3 b^3}\)[/tex]
I hope this step-by-step solution is clear and helpful!
### 1. [tex]\(\frac{2}{a^2 b^3} - \frac{1}{a b}\)[/tex]
First, let's simplify the fraction:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1}{a b} \][/tex]
To combine these fractions, we need a common denominator, which is [tex]\(a^2 b^3\)[/tex]:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1 \cdot a}{a \cdot a b^3} = \frac{2}{a^2 b^3} - \frac{a b^2}{a^2 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{2 - a b^2}{a^2 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{2}{a^2 b^3} - \frac{1}{a b} = \frac{2 - a b^2}{a^2 b^3} \][/tex]
### 2. [tex]\(\frac{1}{a b^2} - \frac{1}{a^3 b}\)[/tex]
Next, we'll handle the second expression:
[tex]\[ \frac{1}{a b^2} - \frac{1}{a^3 b} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^2\)[/tex]:
[tex]\[ \frac{1 \cdot a^2}{a^2 \cdot a b^2} - \frac{1 \cdot b}{a^3 \cdot b b} = \frac{a^2}{a^3 b^2} - \frac{b}{a^3 b^2} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{a^2 - b}{a^3 b^2} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{a b^2} - \frac{1}{a^3 b} = \frac{a^2 - b}{a^3 b^2} \][/tex]
### 3. [tex]\(\frac{2}{a^3 b^3} - \frac{1}{a^2 b^3}\)[/tex]
Simplify the third expression:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^3\)[/tex]:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1 \cdot a}{a \cdot a^2 b^3} = \frac{2}{a^3 b^3} - \frac{a}{a^3 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{2 - a}{a^3 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} = \frac{2 - a}{a^3 b^3} \][/tex]
### 4. [tex]\(\frac{1}{a^3 b^2} - \frac{1}{a^2 b^3}\)[/tex]
Simplify the fourth expression:
[tex]\[ \frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} \][/tex]
Find a common denominator, which is [tex]\(a^3 b^3\)[/tex]:
[tex]\[ \frac{1 \cdot b}{a^3 \cdot b b^2} - \frac{1 \cdot a}{a \cdot a^2 b^3} = \frac{b}{a^3 b^3} - \frac{a}{a^3 b^3} \][/tex]
Now, subtract the numerators:
[tex]\[ = \frac{b - a}{a^3 b^3} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} = \frac{b - a}{a^3 b^3} \][/tex]
### 5. [tex]\(\frac{a^2 - b}{a^3 b^2}\)[/tex]
This expression is already in its simplified form:
[tex]\[ \frac{a^2 - b}{a^3 b^2} \][/tex]
### 6. [tex]\(\frac{b - a}{a^9 b^9}\)[/tex]
This expression is also already simplified in its simplest form:
[tex]\[ \frac{b - a}{a^9 b^9} \][/tex]
### 7. [tex]\(\frac{2 - a b^2}{a^2 b^3}\)[/tex]
This expression is a straightforward fraction and is already in its simplest form:
[tex]\[ \frac{2 - a b^2}{a^2 b^3} \][/tex]
### 8. [tex]\(\frac{2 - a}{a^3 b^3}\)[/tex]
Finally, this expression is also a simplified fraction:
[tex]\[ \frac{2 - a}{a^3 b^3} \][/tex]
Thus, the final simplified forms for these expressions are:
1. [tex]\(\frac{2}{a^2 b^3} - \frac{1}{a b} = \frac{2 - a b^2}{a^2 b^3}\)[/tex]
2. [tex]\(\frac{1}{a b^2} - \frac{1}{a^3 b} = \frac{a^2 - b}{a^3 b^2}\)[/tex]
3. [tex]\(\frac{2}{a^3 b^3} - \frac{1}{a^2 b^3} = \frac{2 - a}{a^3 b^3}\)[/tex]
4. [tex]\(\frac{1}{a^3 b^2} - \frac{1}{a^2 b^3} = \frac{b - a}{a^3 b^3}\)[/tex]
5. [tex]\(\frac{a^2 - b}{a^3 b^2}\)[/tex]
6. [tex]\(\frac{b - a}{a^9 b^9}\)[/tex]
7. [tex]\(\frac{2 - a b^2}{a^2 b^3}\)[/tex]
8. [tex]\(\frac{2 - a}{a^3 b^3}\)[/tex]
I hope this step-by-step solution is clear and helpful!
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.
