Select all possible excluded values of the product: 2m−5⋅
2m+5

4m2−20m+25
.

Question

Select all possible excluded values of the product: 2m−5⋅
2m+5

4m2−20m+25
 .

BlackTom AI · Accepted Answer

We are asked to find all excluded values for the given product expression. The expression appears to be a rational expression where the denominator is 4m^2 − 20m + 25.

First, notice that 4m^2 − 20m + 25 factors as (2m − 5)^2. A rational expression is undefined when its denominator equals zero, so we solve (2m − 5)^2 = 0, which gives 2m − 5 = 0 and thus m = 5/2 (which is the same as 2.5).

Option 1: x = 5/2. This is exactly the value that makes the denominator zero, so it is an excluded value.

Option 2: x = 2.5. This is the decimal representation of 5/2 and represents the same number. Since it corresponds to the same forbidden input where the denominator vanishes, it is also an excluded value.

In summary, the only excluded value is m = 5/2, which can be represented as either 5/2 or 2.5; both options correspond to the same excluded input for the expression.

ALGII141-027 5.2 Practice Problems

Select all possible excluded values of the product: 2m−5⋅ 2m+5 4m2−20m+25 .

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