Question

Math

Posted 4 months ago

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

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Answer from Sia

Posted 4 months ago

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.

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