Question - Simplifying an Algebraic Expression
Solution:
To simplify the given algebraic expression:\[\frac{\frac{2}{x} - 5}{6 + \frac{3}{x}}\]First, find a common denominator for the fractions in the numerator and the denominator. The common denominator for the fractions with $$x$$ in the numerator is $$x$$, and similarly for the denominator.Rewrite the expression with common denominators as follows:\[\frac{\left(\frac{2}{x} - \frac{5x}{x}\right)}{\left(6\frac{x}{x} + \frac{3}{x}\right)}\]This simplifies to:\[\frac{\frac{2 - 5x}{x}}{\frac{6x + 3}{x}}\]Now, since the denominators are the same, the fractions can be combined:\[\frac{2 - 5x}{6x + 3}\]This is the simplified form of the given expression. It cannot be further simplified as there are no common factors between the numerator and the denominator that can be cancelled out.
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