PLEASE HELP ME RATIONALIZE THIS

[yess]

rationalize this numerator so that

[(?2(x+delta x)-3) - (?2x-3)]/delta x = 2/[(?2(x+delta x)-3) + ?2x-3)]

 

[soroban]

Hello, yess!

Where did this problem come from?
There must be a typo . . .

\(\displaystyle \text{Rationalize this numerator so that:}\)

. . . . \(\displaystyle \frac{[\sqrt{2}(x+\Delta x)-3] - [\sqrt{2}x-3]} {\Delta x} \;=\; \frac{2}{[\sqrt{2}(x+\Delta x)-3] + [\sqrt{2}x-3]}\)

This is not true . . .

The left side is the Difference Quotient for: .\(\displaystyle f(x) \:=\:\sqrt{2}\,x - 3\)

I can't imagine why anyone would want to rationalize the numerator.
. . (And get the wrong result.)