### the value of x for which x 2/x^2-2x-10?

the value of x for which x 2/x^2-2x-10?

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x ± 2 / x² - 2x - 10= 1/0 (undefined)
So, cross multiplying, we will be left with:
x² - 2x - 10= 0
a= 1, b = - 2; c= - 10
x= [ - b ± √(b² - 4ac) ] / 2a
= [ - (- 2) ± √((- 2)² - 4(1)(-10) ] / 2(1)
= [ 2 ± √(4 + 40) ] / 2
= [ 2 ± √44 ] / 2
= (2 + √(4 × 11)) / 2
= (2 + 2√11)/2
= 1 + √11

Thus, the value of x is (1 + √11), when the expression, (x ± 2 / x² - 2x - 10) is undefined.

x ± 2 / x² - 2x - 10= 0/1 (defined)
x ± 2= 0
x + 2= 0 or x - 2= 0
x + 2 - 2= 0 - 2 or x - 2 + 2= 0 + 2
x + 0= - 2 or x - 0= + 2
x= - 2 or x= +2

Therefore, the value of x is either - 2 or +2 when the expression, (x ± 2 / x² - 2x - 10) is defined.

Thank you.
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