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Maths-

SAT

Easy

Question

$fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction$
Which of the following is equivalent to the expression above for x≠ $square root of 2$ ?

x - 1
x + 1
$x - \sqrt{2}$
$x + \sqrt{2}$

The correct answer is: $x plus square root of 2$

$fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction equals fraction numerator x squared minus left parenthesis square root of 2 right parenthesis squared over denominator x minus square root of 2 end fraction equals fraction numerator left parenthesis x minus square root of 2 right parenthesis left parenthesis x plus square root of 2 right parenthesis over denominator left parenthesis x minus square root of 2 right parenthesis end fraction equals x plus square root of 2$

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