What are the excluded values? 1.)0 and 15 2.)3 and -5 and 5

Denominator of a rational expression cannot be 0 because if it will be 0 then the expression will be undefined. Hence, we need to exclude the values of x at which the denominator will be 0. So,

x²-2x-15=0

We can solve this equation by factoring the trinomial on the left side of the equation.

For that we need to find the two multiples of the constant term -15 so that their addition will result the coefficient of -2.

So, -15= -5*3 and -5+3=-2.

So, we can replace -2x with -5x+3x in the above equation.

x²-5x+3x-15=0

(x²-5x)+(3x-15)=0 Making the group of two terms.

x(x - 5) + 3(x - 5) =0 Taking out the common factor from each terms.

(x - 5) (x + 3) =0 Taking out the common factor (x-5) from both the terms.

So, x - 5 =0 and x + 3 =0 Set up each factor equal to 0.

So, x=5 and x=-3.

Hence, the excluded values are 3) -3 and 5.

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