Question

simplify. express your answer as a single fraction in simplest form.
$u + 7 - \frac{2}{u^{4}}$

Explanation:

Step1: Find a common denominator

To combine the terms \(u + 7\) and \(-\frac{2}{u^{4}}\) into a single fraction, we need a common denominator. The common denominator will be \(u^{4}\) since \(u + 7\) can be written with a denominator of \(u^{4}\) by multiplying the numerator and denominator of \(u + 7\) by \(u^{4}\). So we have:
\(u + 7=\frac{(u + 7)\times u^{4}}{u^{4}}=\frac{u^{5}+7u^{4}}{u^{4}}\)

Step2: Subtract the fraction

Now we subtract \(\frac{2}{u^{4}}\) from \(\frac{u^{5}+7u^{4}}{u^{4}}\). When subtracting fractions with the same denominator, we subtract the numerators:
\(\frac{u^{5}+7u^{4}}{u^{4}}-\frac{2}{u^{4}}=\frac{u^{5}+7u^{4}-2}{u^{4}}\)

Answer:

\(\frac{u^{5}+7u^{4}-2}{u^{4}}\)