Answered

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Find the difference. Express your answer in simplest form.

[tex]\[ \frac{u-8}{u+1} - \frac{-7u+4}{u+1} \][/tex]

Click on the correct answer.
A. [tex]\(\frac{-6u+4}{u+1}\)[/tex]
B. [tex]\(\frac{-6u+4}{2u+2}\)[/tex]
C. [tex]\(\frac{8u-12}{2u+2}\)[/tex]
D. [tex]\(\frac{8u-12}{u+1}\)[/tex]

Sagot :

GinnyAnswer
Sure, let's solve the problem step-by-step.

Given the expression:
[tex]\[ \frac{u-8}{u+1}-\frac{-7u+4}{u+1} \][/tex]

Since both fractions have the same denominator [tex]\(u + 1\)[/tex], we can combine them into a single fraction:
[tex]\[ \frac{(u-8) - (-7u+4)}{u+1} \][/tex]

Now, we simplify the numerator:
[tex]\[ (u - 8) - (-7u + 4) = u - 8 + 7u - 4 \][/tex]

Combine like terms in the numerator:
[tex]\[ u + 7u - 8 - 4 = 8u - 12 \][/tex]

So we now have:
[tex]\[ \frac{8u - 12}{u+1} \][/tex]

This is the simplified form of the original expression. Therefore, the correct answer is:
[tex]\[ \frac{8u-12}{u+1} \][/tex]

Click on the correct answer:

[tex]\[ \boxed{\frac{8u-12}{u+1}} \][/tex]
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