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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{7xy^{2}}$ $-$ $9$

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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{5}{7xy^{2}}

-

9

Rewrite as fraction: $\frac{5}{7xy^2} - 9$ $\newline$ Rewrite $9$ as a fraction with the same denominator as the first term. $\newline$ $\frac{5}{7xy^2} - \frac{9}{1}$ $\newline$ To find a common denominator, we can multiply $9$ by $\frac{7xy^2}{7xy^2}$ . $\newline$ $\frac{5}{7xy^2} - \frac{9\times(7xy^2)}{1\times7xy^2}$
Find common denominator: $\frac{5}{7xy^2} - \frac{9\times(7xy^2)}{1\times7xy^2}$ $\newline$ Perform the multiplication in the second term. $\newline$ $\frac{5}{7xy^2} - \frac{(9\times7xy^2)}{7xy^2}$ $\newline$ $\frac{5}{7xy^2} - \frac{63xy^2}{7xy^2}$
Perform multiplication: $\frac{5}{7}xy^2 - \frac{63xy^2}{7xy^2}$ $\newline$ Combine the two fractions over the common denominator. $\newline$ $\frac{(5 - 63xy^2)}{(7xy^2)}$
Combine fractions: $5 - 63xy^2$ cannot be simplified further because there are no common factors between $5$ and $63xy^2$ . So the final simplified expression is: $\frac{5 - 63xy^2}{7xy^2}$

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