Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{b^4c}{3} - c$

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{b^4c}{3} - c

Identify Common Denominator: Identify the common denominator for the two terms. $\newline$ Since the first term has a denominator of $3$ and the second term can be thought of as $c/1$ , the common denominator is $3$ .
Express Second Term: Express the second term with the common denominator. $\newline$ To do this, multiply the numerator and denominator of $c$ by $3$ to get the equivalent fraction $\frac{3c}{3}$ .
Rewrite with Common Denominator: Rewrite the expression with the common denominator. $\newline$ The expression now becomes $(b^4c)/3 - 3c/3$ .
Combine Terms: Combine the terms over the common denominator. $\newline$ Since both terms now have the same denominator, we can combine them as follows: $\newline$ $(b^4c - 3c)/3$
Factor Out Common Factor: Factor out the common factor in the numerator. $\newline$ We can factor out $c$ from the numerator to simplify the expression further: $\newline$ $\frac{c(b^4 - 3)}{3}$
Check for Further Simplification: Check if the fraction can be simplified further. $\newline$ Since there are no common factors between the numerator and the denominator, the fraction is already in its simplest form.