Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
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!
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
