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Maths-

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Question

Explain $fraction numerator 4 x squared minus 7 over denominator 4 x squared minus 7 end fraction$ =1 why is a valid identity under the domain of all real numbers except $plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$ .

hint Hint:

When we cancel expressions which are common to numerator and the denominator, we must exclude values for which the denominator attains its zero as dividing with zero is not defined.
We are asked to find why the domain of the given expression is all real numbers expect $plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$ .

The correct answer is: Hence, the domain is set of all real numbers excludingplus-or-minus fraction numerator square root of 7 over denominator 2 end fraction.

Step 1 of 1:
When we find the domain of a rational expression, we have to exclude the values for which the denominator attains a zero value. This is because, when the denominator gets a zero value, the expression gets divided by zero which is not defined.
Here, the expression is: $fraction numerator 4 x squared minus 7 over denominator 4 x squared minus 7 end fraction equals 1$
The value for which the denominator gets a zero value is:
$4 x squared minus 7 equals 0$
$4 x squared equals 7$
$x squared equals 7 over 4$
$x equals plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$
Thus, the values are: $plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$ which we have to exclude.
Hence, the domain is set of all real numbers excluding $plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$ .

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