Question

simplify. express your answer as a single fraction in simplest form.
$3a - 7 + \frac{4}{a^3b}$

Explanation:

Step1: Find a common denominator

The terms are \(3a - 7\) (which can be thought of as having a denominator of \(1\)) and \(\frac{4}{a^{3}b}\). The common denominator will be \(a^{3}b\).

Step2: Rewrite \(3a - 7\) with the common denominator

Multiply \(3a - 7\) by \(\frac{a^{3}b}{a^{3}b}\):

$$ (3a - 7)\times\frac{a^{3}b}{a^{3}b}=\frac{(3a - 7)a^{3}b}{a^{3}b}=\frac{3a^{4}b-7a^{3}b}{a^{3}b} $$

Step3: Add the two fractions

Now add \(\frac{3a^{4}b - 7a^{3}b}{a^{3}b}\) and \(\frac{4}{a^{3}b}\):

$$ \frac{3a^{4}b-7a^{3}b}{a^{3}b}+\frac{4}{a^{3}b}=\frac{3a^{4}b - 7a^{3}b + 4}{a^{3}b} $$

Answer:

\(\frac{3a^{4}b - 7a^{3}b + 4}{a^{3}b}\)