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Sagot :
The values of x for which the expression [tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]is undefined are 0,[tex]\sqrt{41} /2[/tex] and imaginary numbers.
Given Expression :x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x
We have to find out those values of x for which the expression does not exists.
[tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]
We have to take LCM of the expression which is equal to [tex]x^{3}(x^{2}-x-10)(2x^{2} +4x^{3})[/tex]
LCM is the smallest positive integer that is divisible by both the numbers whose LCM is found.
and it is present in the denominator.
Expression if exists cannot take denominator equal to 0.
So, by putting LCM equal to zero we find
x=0,x=imaginary numbers and x=[tex]\sqrt{41} /2[/tex].
Hence the given expression have not take values of x=0,[tex]\sqrt{41} /2[/tex], imaginary number.
Learn more about expressions at https://brainly.com/question/723406
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