Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To simplify the given expression [tex]\(\frac{4 x}{3 a b^3}+\frac{2 y}{4 a^2 b^2}\)[/tex], we will follow these steps:
1. Simplify each term individually, if possible.
2. Find a common denominator for the fractions.
3. Combine the fractions into a single expression.
4. Simplify the resulting expression.
Let's start by simplifying each term.
The first term is [tex]\(\frac{4 x}{3 a b^3}\)[/tex].
The second term is [tex]\(\frac{2 y}{4 a^2 b^2}\)[/tex]. Notice that [tex]\(\frac{2 y}{4}\)[/tex] simplifies to [tex]\(\frac{y}{2}\)[/tex]. So, we can rewrite the second term as [tex]\(\frac{y}{2 a^2 b^2}\)[/tex].
Now the expression is:
[tex]\[ \frac{4 x}{3 a b^3} + \frac{y}{2 a^2 b^2} \][/tex]
Next, we need to find a common denominator for the two fractions. The denominators are [tex]\(3 a b^3\)[/tex] and [tex]\(2 a^2 b^2\)[/tex]. The least common multiple (LCM) of these denominators is:
[tex]\[ \text{LCM}(3 a b^3, 2 a^2 b^2) = 6 a^2 b^3 \][/tex]
Now we convert each fraction to have this common denominator.
For the first term [tex]\(\frac{4 x}{3 a b^3}\)[/tex], we need to multiply the numerator and the denominator by [tex]\(2 a\)[/tex]:
[tex]\[ \frac{4 x \cdot 2 a}{3 a b^3 \cdot 2 a} = \frac{8 a x}{6 a^2 b^3} \][/tex]
For the second term [tex]\(\frac{y}{2 a^2 b^2}\)[/tex], we need to multiply the numerator and the denominator by [tex]\(3 b\)[/tex]:
[tex]\[ \frac{y \cdot 3 b}{2 a^2 b^2 \cdot 3 b} = \frac{3 b y}{6 a^2 b^3} \][/tex]
Now the expression is:
[tex]\[ \frac{8 a x}{6 a^2 b^3} + \frac{3 b y}{6 a^2 b^3} \][/tex]
Since both fractions now have the same denominator, we can combine them:
[tex]\[ \frac{8 a x + 3 b y}{6 a^2 b^3} \][/tex]
This is the simplified form of the given expression. Therefore, the final answer is:
[tex]\[ \frac{8 a x + 3 b y}{6 a^2 b^3} \][/tex]
1. Simplify each term individually, if possible.
2. Find a common denominator for the fractions.
3. Combine the fractions into a single expression.
4. Simplify the resulting expression.
Let's start by simplifying each term.
The first term is [tex]\(\frac{4 x}{3 a b^3}\)[/tex].
The second term is [tex]\(\frac{2 y}{4 a^2 b^2}\)[/tex]. Notice that [tex]\(\frac{2 y}{4}\)[/tex] simplifies to [tex]\(\frac{y}{2}\)[/tex]. So, we can rewrite the second term as [tex]\(\frac{y}{2 a^2 b^2}\)[/tex].
Now the expression is:
[tex]\[ \frac{4 x}{3 a b^3} + \frac{y}{2 a^2 b^2} \][/tex]
Next, we need to find a common denominator for the two fractions. The denominators are [tex]\(3 a b^3\)[/tex] and [tex]\(2 a^2 b^2\)[/tex]. The least common multiple (LCM) of these denominators is:
[tex]\[ \text{LCM}(3 a b^3, 2 a^2 b^2) = 6 a^2 b^3 \][/tex]
Now we convert each fraction to have this common denominator.
For the first term [tex]\(\frac{4 x}{3 a b^3}\)[/tex], we need to multiply the numerator and the denominator by [tex]\(2 a\)[/tex]:
[tex]\[ \frac{4 x \cdot 2 a}{3 a b^3 \cdot 2 a} = \frac{8 a x}{6 a^2 b^3} \][/tex]
For the second term [tex]\(\frac{y}{2 a^2 b^2}\)[/tex], we need to multiply the numerator and the denominator by [tex]\(3 b\)[/tex]:
[tex]\[ \frac{y \cdot 3 b}{2 a^2 b^2 \cdot 3 b} = \frac{3 b y}{6 a^2 b^3} \][/tex]
Now the expression is:
[tex]\[ \frac{8 a x}{6 a^2 b^3} + \frac{3 b y}{6 a^2 b^3} \][/tex]
Since both fractions now have the same denominator, we can combine them:
[tex]\[ \frac{8 a x + 3 b y}{6 a^2 b^3} \][/tex]
This is the simplified form of the given expression. Therefore, the final answer is:
[tex]\[ \frac{8 a x + 3 b y}{6 a^2 b^3} \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.