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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{7wx^5}{4} - \frac{4}{7x^3}$

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Add and subtract rational expressions

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

\newline

\frac{7wx^5}{4} - \frac{4}{7x^3}

Identify Common Denominator: Identify the common denominator for the two fractions. $\newline$ Since the fractions have different denominators, we need to find a common denominator to combine them. The first fraction has a denominator of $4$ , and the second fraction has a denominator of $7x^3$ . The least common denominator (LCD) will be the product of these two denominators, which is $4 \times 7x^3 = 28x^3$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator. $\newline$ We will multiply the numerator and denominator of each fraction by whatever is necessary to get the denominator to be the LCD. $\newline$ For the first fraction, $\frac{7wx^5}{4}$ , we need to multiply the numerator and denominator by $7x^3$ to get the common denominator of $28x^3$ . $\newline$ $(\frac{7wx^5}{4}) \cdot (\frac{7x^3}{7x^3}) = \frac{49wx^8}{28x^3}$ $\newline$ For the second fraction, $\frac{4}{7x^3}$ , we need to multiply the numerator and denominator by $4$ to get the common denominator of $28x^3$ . $\newline$ $(\frac{4}{7x^3}) \cdot (\frac{4}{4}) = \frac{16}{28x^3}$
Combine Fractions: Combine the fractions. $\newline$ Now that both fractions have the same denominator, we can combine them by subtracting the numerators. $\newline$ $(\frac{49wx^8}{28x^3}) - (\frac{16}{28x^3}) = \frac{49wx^8 - 16}{28x^3}$
Simplify Expression: Simplify the expression if possible. $\newline$ In this case, there are no common factors between the numerator and the denominator that can be canceled out, so the expression is already in its simplest form. $\newline$ $(49wx^8 - 16)/28x^3$ is the simplified expression.

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