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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{4}{b^4} - \frac{4}{9bc^4}$

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Add and subtract rational expressions

Full solution

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

\newline

\frac{4}{b^4} - \frac{4}{9bc^4}

Identify common denominator: Identify the common denominator. $\newline$ The common denominator for the fractions $\frac{4}{b^4}$ and $\frac{4}{9bc^4}$ is $9b^4c^4$ because it is the least common multiple of $b^4$ and $9bc^4$ .
Rewrite with common denominator: Rewrite each fraction with the common denominator. $\newline$ To rewrite $\frac{4}{b^4}$ with the common denominator, multiply both the numerator and the denominator by $9c^4$ . To rewrite $\frac{4}{9bc^4}$ with the common denominator, multiply both the numerator and the denominator by $b^3$ . $\newline$ $\frac{4}{b^4} = \frac{4 \times 9c^4}{b^4 \times 9c^4}$ $\newline$ $\frac{4}{9bc^4} = \frac{4 \times b^3}{9bc^4 \times b^3}$
Perform multiplications: Perform the multiplications. $\newline$ Now, perform the multiplications to get the equivalent fractions with the common denominator. $\newline$ $\frac{4}{b^4} = \frac{4 \times 9c^4}{9b^4c^4}$ $\newline$ $\frac{4}{9bc^4} = \frac{4 \times b^3}{9b^4c^4}$
Combine fractions: Combine the fractions. $\newline$ Now that we have a common denominator, we can combine the fractions by subtracting the numerators. $\newline$ $(4 \times 9c^4)/(9b^4c^4) - (4 \times b^3)/(9b^4c^4)$ $\newline$ = $(36c^4 - 4b^3)/(9b^4c^4)$
Simplify numerator: Simplify the numerator. Simplify the numerator by combining like terms, if possible. In this case, there are no like terms to combine, so the numerator remains as is. $(36c^4 - 4b^3)/(9b^4c^4)$
Check for simplification: Check for any further simplification. $\newline$ There is no further simplification possible because the terms in the numerator do not have common factors with the denominator. $\newline$ Final answer: $(36c^4 - 4b^3)/(9b^4c^4)$

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