Question

Subtract the rational expression

Please show steps

Answer 1

Answer:
`-x^2-3x+46/x^2+4x-32`

Explanation:

Answer 2

`(-x^2-3x+46)/(x^2+4x-32)`

Explanation:

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

`(6)/(x^2+4x-32)-(x-5)/(x-4)`

Common denominator

Both terms can be expressed using the same denominator, then summed.

`(6)/(x^2+4x-32)-(x-5)/(x-4)=(6)/((x-4)(x+8))-((x-5)(x+8))/((x-4)(x+8))\\\\\\=(6-(x-5)(x+8))/((x-4)(x+8))=(6-(x^2+3x-40))/((x-4)(x+8))=\boxed{(-x^2-3x+46)/(x^2+4x-32)}`

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Additional comment

The process is fundamentally identical to finding the difference of numerical fractions. The least common denominator is found by considering factors of the denominators, just as it would be if they were pure numbers.

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