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Which is the simplified rational expression for r^2 −4r+5/ r−4 - r^2 ÷ 2r−8/ r-4 ?

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Final answer:

To simplify the given rational expression, factor the denominators, find the common denominator, combine the expressions, and simplify by combining like terms and reducing. The expression simplifies to (r^2 - 4r + 5) / (r - 4) - (r^2 / 2).

Step-by-step explanation:

The student's question involves simplifying a complex rational expression:

r^2 - 4r + 5 / (r - 4) - r^2 ÷ (2r - 8) / (r - 4)

To simplify this expression, we have to follow several steps:

Factor the denominators if possible.

Find a common denominator.

Combine the rational expressions.

Simplify the result by combining like terms and reducing.

The denominators (r - 4) and (2r - 8), can be simplified since 2r - 8 is 2(r - 4), hence they have a common factor.

Since division by a fraction is equivalent to multiplication by its reciprocal, the expression becomes:

(r^2 - 4r + 5) / (r - 4) - (r^2) / (2(r - 4)) × (r - 4)

After multiplying the second term by the reciprocal, we combine like terms:

(r^2 - 4r + 5) / (r - 4) - (r^2 / 2)

Simplifying further, the rational expression is reduced.

User Minal
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