Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Select the correct answer.

What is this expression in simplest form?
[tex]\[
\frac{4w}{w-2} + \frac{3w}{w-3}
\][/tex]

A. [tex]\(\frac{7w^2 - 5}{w^2 - 5w + 6}\)[/tex]

B. [tex]\(\frac{7w}{w^2 + 6}\)[/tex]

C. [tex]\(\frac{7w^2 - 18w}{w^2 - 5w + 6}\)[/tex]

D. [tex]\(\frac{7\psi}{2w - 5}\)[/tex]


Sagot :

To simplify the given expression:

[tex]\[ \frac{4w}{w-2} + \frac{3w}{w-3} \][/tex]

we need to find a common denominator and combine the fractions. The common denominator of the two fractions is [tex]\((w - 2)(w - 3)\)[/tex]. First, we rewrite each fraction with the common denominator:

[tex]\[ \frac{4w}{w-2} = \frac{4w(w-3)}{(w-2)(w-3)} \][/tex]
and
[tex]\[ \frac{3w}{w-3} = \frac{3w(w-2)}{(w-2)(w-3)} \][/tex]

Next, we combine the two fractions:

[tex]\[ \frac{4w(w-3) + 3w(w-2)}{(w-2)(w-3)} \][/tex]

We will now distribute within the numerators:

[tex]\[ 4w(w-3) = 4w^2 - 12w \][/tex]
[tex]\[ 3w(w-2) = 3w^2 - 6w \][/tex]

Adding these together:

[tex]\[ 4w^2 - 12w + 3w^2 - 6w = 7w^2 - 18w \][/tex]

So, combining these into one fraction, we have:

[tex]\[ \frac{7w^2 - 18w}{(w-2)(w-3)} \][/tex]

The denominator can be factored as follows:

[tex]\[ (w-2)(w-3) = w^2 - 5w + 6 \][/tex]

Thus, the combined fraction is:

[tex]\[ \frac{7w^2 - 18w}{w^2 - 5w + 6} \][/tex]

Among the provided choices:

A. [tex]\(\frac{7w^2 - 5}{w^2 - 5w + 6}\)[/tex]
B. [tex]\(\frac{7w}{w^2 + 6}\)[/tex]
C. [tex]\(\frac{7w^2 - 18w}{w^2 - 5w + 6}\)[/tex]
D. [tex]\(\frac{7 \psi}{2w - 5}\)[/tex]

Option C, [tex]\(\frac{7w^2 - 18w}{w^2 - 5w + 6}\)[/tex], matches our result.

Therefore, the correct answer is:

C. [tex]\(\frac{7w^2 - 18w}{w^2 - 5w + 6}\)[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.