Calculus AP

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i wanna KNOW IF im DOING RIGHT.

Evaluate the difference quotient for the given function. Simplify your answer.
f(x)=x+3/x+1, [f(x)-f(1)]/(x-1)

simplify my answer:
[(x+3)/(x+1) - (1+3)/(1+1)]/(x-1)

= [x+3/x+1 - 4/2] / (x-1)

= [2(x+3)-4(x+1)/2(x+1)] / (x-1)

= [2x+6-4x-4/2(x+1)] / (x-1)

= [-2x+2x/2(x+1)] /(x-1)

= [-2(x-1)/2(x+1)]/(x-1)
so my answer is -1

  • Calculus AP -

    i mean my answer is -1/(x+1)

  • Calculus AP -

    correct,
    but why didn't you reduce the 4/2 in the second step to 2, it would have made the algebra a lot easier.

  • Calculus AP -

    oh 4/2 is 2. ok
    thanks

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