Question

Subtract the rational expression

Please show steps

Answer 1

1/(x -2)

Explanation:

You want the simplified form of the rational expression ...

`(1)/(x-4)-(2)/(x^2-6x+8)`

Simplification

We simplify this by combining terms over a common denominator, then cancelling any common factors from numerator and denominator.

`(1)/(x-4)-(2)/(x^2-6x+8) = ((x-2))/((x-4)(x-2))-(2)/((x-4)(x-2))\\\\\\=((x-2)-2)/((x-4)(x-2))=(x-4)/((x-4)(x-2))=\boxed{(1)/(x-2)}`

Note that the domain still excludes x=4, in addition to the obvious exclusion of x=2.

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