Answer:
4) x minus 3 over the quantity x times x minus 1
Step-by-step explanation:
The sum of rational expressions is found the same way the sum of numerical fractions is found. Each part of the sum must be expressed using a common denominator. Then the numerators can be added.
We want to simplify ...
[tex]\dfrac{1}{x}-\dfrac{2}{x^2-x}[/tex]
For the purpose of finding a common denominator, it is useful to have each denominator in factored form:
[tex]\dfrac{1}{x}-\dfrac{2}{x(x-1)}[/tex]
This lets us see that the product of unique denominator factors is x(x-1), so that will be the common denominator we want to use.
[tex]=\dfrac{1}{x}\cdot\dfrac{x-1}{x-1}-\dfrac{2}{x(x-1)}=\dfrac{(x-1)-2}{x(x-1)}[/tex]
The expression is simplified by simplifying the numerator and cancelling any common factors from numerator and denominator. We find there are no common factors, so the simplified form is ...
[tex]=\boxed{\dfrac{x-3}{x(x-1)}}[/tex]
