Write the following as a single rational expression.
$$
\frac{1}{x}-\frac{1}{x-2}
$$

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To combine the fractions $\frac{1}{x}$ and $\frac{1}{x-2}$ into a single rational expression, we need a common denominator. The common denominator for $x$ and $x-2$ is $x(x-2)$. ‖ ‖ step 2 ⋮ Rewrite each fraction with the common denominator: $\frac{1}{x} = \frac{(x-2)}{x(x-2)}$ and $\frac{1}{x-2} = \frac{x}{x(x-2)}$. ‖ ‖ step 3 ⋮ Subtract the two fractions: $\frac{(x-2)}{x(x-2)} - \frac{x}{x(x-2)} = \frac{(x-2) - x}{x(x-2)}$. ‖ ‖ step 4 ⋮ Simplify the numerator: $(x-2) - x = -2$. ‖ ‖ step 5 ⋮ Combine the simplified numerator with the common denominator: $\frac{-2}{x(x-2)}$. ‖ ∻Answer∻ ⚹ $\frac{-2}{x(x-2)}$ ⚹ ∻Key Concept∻ ⚹Combining Fractions⚹ ∻Explanation∻ ⚹To combine fractions, find a common denominator, rewrite each fraction with this common denominator, and then perform the necessary arithmetic operations on the numerators.⚹◊How can you rewrite the expression $\frac{1}{x}-\frac{1}{x-2}$ as a single rational expression?⍭ Generate me a similar question◊

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