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Find the difference. Express your answer in simplest form.

[tex]\[ \frac{u+2}{u-3} - \frac{-2u-7}{u-3} \][/tex]

Click on the correct answer.

[tex]\[
\begin{array}{cc}
\frac{u+5}{2u-6} & \frac{u+5}{u-3} \\
\frac{3u+9}{u-3} & \frac{3u+9}{2u-6}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To find the difference between the given fractions and express it in simplest form, follow these steps:

1. Write the original problem:

[tex]\[ \frac{u+2}{u-3} - \frac{-2u-7}{u-3} \][/tex]

2. Since both fractions have the same denominator, subtract the numerators directly:

[tex]\[ \frac{(u+2) - (-2u-7)}{u-3} \][/tex]

3. Simplify the numerator:

[tex]\[ (u+2) - (-2u-7) = u + 2 + 2u + 7 = u + 2u + 2 + 7 = 3u + 9 \][/tex]

4. Combine the simplified numerator over the common denominator:

[tex]\[ \frac{3u + 9}{u-3} \][/tex]

5. Factor out the greatest common factor in the numerator (if possible):

Notice that [tex]\(3u + 9\)[/tex] can be factored:

[tex]\[ 3(u + 3) \][/tex]

So, the fraction becomes:

[tex]\[ \frac{3(u + 3)}{u-3} \][/tex]

This is the simplified form of the given expression. Therefore, the correct answer is:

[tex]\[ \frac{3(u+3)}{u-3} \][/tex]
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