Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To simplify the expression
[tex]\[ \frac{p^2 + pq + q^2}{p + q} - \frac{p^2 - pq + q^2}{p + q}, \][/tex]
we proceed as follows:
1. Combine the fractions over a common denominator:
Both fractions have the same denominator, [tex]\( p + q \)[/tex]. Therefore, we can combine them into a single fraction:
[tex]\[ \frac{(p^2 + pq + q^2) - (p^2 - pq + q^2)}{p + q}. \][/tex]
2. Simplify the numerator by distributing and combining like terms:
Let's expand the numerator:
[tex]\[ (p^2 + pq + q^2) - (p^2 - pq + q^2). \][/tex]
Distribute the negative sign through the terms inside the second parenthesis:
[tex]\[ p^2 + pq + q^2 - p^2 + pq - q^2. \][/tex]
Combine like terms. Notice that [tex]\( p^2 - p^2 \)[/tex] and [tex]\( q^2 - q^2 \)[/tex] cancel out:
[tex]\[ pq + pq = 2pq. \][/tex]
So, the numerator simplifies to [tex]\( 2pq \)[/tex].
3. Form the simplified fraction:
Now, we have the simplified numerator over the common denominator:
[tex]\[ \frac{2pq}{p + q}. \][/tex]
Therefore, the expression simplifies to:
[tex]\[ \frac{2pq}{p + q}. \][/tex]
[tex]\[ \frac{p^2 + pq + q^2}{p + q} - \frac{p^2 - pq + q^2}{p + q}, \][/tex]
we proceed as follows:
1. Combine the fractions over a common denominator:
Both fractions have the same denominator, [tex]\( p + q \)[/tex]. Therefore, we can combine them into a single fraction:
[tex]\[ \frac{(p^2 + pq + q^2) - (p^2 - pq + q^2)}{p + q}. \][/tex]
2. Simplify the numerator by distributing and combining like terms:
Let's expand the numerator:
[tex]\[ (p^2 + pq + q^2) - (p^2 - pq + q^2). \][/tex]
Distribute the negative sign through the terms inside the second parenthesis:
[tex]\[ p^2 + pq + q^2 - p^2 + pq - q^2. \][/tex]
Combine like terms. Notice that [tex]\( p^2 - p^2 \)[/tex] and [tex]\( q^2 - q^2 \)[/tex] cancel out:
[tex]\[ pq + pq = 2pq. \][/tex]
So, the numerator simplifies to [tex]\( 2pq \)[/tex].
3. Form the simplified fraction:
Now, we have the simplified numerator over the common denominator:
[tex]\[ \frac{2pq}{p + q}. \][/tex]
Therefore, the expression simplifies to:
[tex]\[ \frac{2pq}{p + q}. \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.