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Simplify. Express your answer as a single fraction in simplest form. \newliney3−35x\frac{y}{3} - \frac{3}{5}x

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newliney3−35x\frac{y}{3} - \frac{3}{5}x
  1. Identify Common Denominator: Identify the common denominator for the fractions y3\frac{y}{3} and 35x\frac{3}{5x}. Since the denominators are 33 and 5x5x, the least common denominator (LCD) is 3×5x3\times 5x.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator.\newlineThe first fraction y3\frac{y}{3} is equivalent to y×5x3×5x\frac{y\times 5x}{3\times 5x}, and the second fraction 35x\frac{3}{5x} is equivalent to 3×33×5x\frac{3\times 3}{3\times 5x}.
  3. Combine Fractions: Combine the fractions over the common denominator.\newline(y⋅5x3⋅5x)−(3⋅33⋅5x)=5xy−915x(\frac{y\cdot 5x}{3\cdot 5x}) - (\frac{3\cdot 3}{3\cdot 5x}) = \frac{5xy - 9}{15x}
  4. Simplify Expression: Simplify the expression if possible.\newlineIn this case, the numerator 5xy−95xy - 9 and the denominator 15x15x cannot be simplified further as there are no common factors to cancel out.

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