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Simplify. Express your answer as a single fraction in simplest form. \newline15u−37tu\frac{1}{5u} - \frac{3}{7tu}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline15u−37tu\frac{1}{5u} - \frac{3}{7tu}
  1. Identify LCD: 15u−37tu\frac{1}{5u} - \frac{3}{7tu}\newlineIdentify the least common denominator (LCD) for the fractions.\newlineThe LCD for 5u5u and 7tu7tu is 35tu35tu.
  2. Rewrite fractions: 15u−37tu\frac{1}{5u} - \frac{3}{7tu}\newlineRewrite each fraction with the LCD as the denominator.\newline(1×7t5u×7t)−(3×57tu×5)\left(\frac{1 \times 7t}{5u \times 7t}\right) - \left(\frac{3 \times 5}{7tu \times 5}\right)\newline=7t35tu−1535tu=\frac{7t}{35tu} - \frac{15}{35tu}
  3. Combine fractions: (7t35tu)−(1535tu)(\frac{7t}{35tu}) - (\frac{15}{35tu})\newlineCombine the fractions over the common denominator.\newline(7t−1535tu)(\frac{7t - 15}{35tu})
  4. Simplify expression: (7t−15)/(35tu)(7t - 15)/(35tu)\newlineSimplify the expression if possible.\newlineThe numerator cannot be simplified further, and the denominator is already in simplest form.\newlineSo, the final answer is (7t−15)/(35tu)(7t - 15)/(35tu).

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