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Simplify. Express your answer as a single fraction in simplest form. \newline8wx5−5w\frac{8wx}{5} - \frac{5}{w}

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline8wx5−5w\frac{8wx}{5} - \frac{5}{w}
  1. Identify common denominator: Identify the common denominator for the fractions.\newlineTo combine the fractions, we need a common denominator. The denominators are currently 55 and ww, so the common denominator will be 5w5w.
  2. Rewrite with common denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction already has a denominator of 55, so we multiply the numerator and denominator of the second fraction by 55 to get the common denominator of 5w5w.\newline8wx5−(5×5)(w×5)\frac{8wx}{5} - \frac{(5 \times 5)}{(w \times 5)}\newline8wx5−255w\frac{8wx}{5} - \frac{25}{5w}
  3. Combine fractions: Combine the fractions.\newlineNow that we have a common denominator, we can combine the numerators.\newline(8wx⋅w)/(5⋅w)−255w(8wx \cdot w)/(5 \cdot w) - \frac{25}{5w}\newlineSince 8wx⋅w8wx \cdot w is 8wx28wx^2, the combined fraction is:\newline(8wx2−25)/5w(8wx^2 - 25)/5w
  4. Simplify expression: Simplify the expression, if possible.\newlineIn this case, the numerator and the denominator do not have any common factors other than 11, so the expression is already in its simplest form.\newlineFinal expression: (8wx2−25)/5w(8wx^2 - 25)/5w

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