Subjects algebra

Fraction Subtraction 37F997

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1. **State the problem:** Simplify the expression $$\frac{2}{f(x)} - \frac{5}{g(x)}$$ as a single fraction in terms of $x$. 2. **Formula and rules:** To subtract fractions, find a common denominator. The common denominator for $$\frac{2}{f(x)}$$ and $$\frac{5}{g(x)}$$ is $$f(x) \cdot g(x)$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{2}{f(x)} = \frac{2 \cdot g(x)}{f(x) \cdot g(x)}$$ $$\frac{5}{g(x)} = \frac{5 \cdot f(x)}{f(x) \cdot g(x)}$$ 4. **Subtract the numerators:** $$\frac{2 \cdot g(x)}{f(x) \cdot g(x)} - \frac{5 \cdot f(x)}{f(x) \cdot g(x)} = \frac{2g(x) - 5f(x)}{f(x)g(x)}$$ 5. **Final answer:** The simplified single fraction is $$\boxed{\frac{2g(x) - 5f(x)}{f(x)g(x)}}$$ This expression is now a single fraction in terms of $x$.