Simplify the expression f(x+h)-f(x)/h when f(x)=2/x+4

Answer 1

Substitute:

2/(x+h) + 4 - ( 2 / x + 4 )

2/(x+h) + 4 - 2/x - 4 = 2/(x + h ) - 2/x find the common denominator x ( x + h )

numerator is 2x -2x -2h

denominator is x^2 + xh

you get -2h / ( x^2 + xh ) Then divide by h you get

-2 /(x^2 +xh )

If h goes to zero, you get -2/x^2

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