Question

Evaluate the difference quotient
f(x)-f(1)/X-1, where f(x)=X +5/x+1

Answer 1

C)
`\displaystyle(-2)/((x+1))`

Explanation:

`\displaystyle (f(x)-f(1))/(x-1)\\ \\((x+5)/(x+1)-(1+5)/(1+1))/(x-1)\\ \\((x+5)/(x+1)-(6)/(2))/(x-1)\\\\((2(x+5))/(2(x+1))-(6(x+1))/(2(x+1)))/(x-1)\\\\((2(x+5)-6(x+1))/(2(x+1)))/(x-1)\\\\((2x+10-6x-6)/(2(x+1)))/(x-1)\\\\((-4x+4)/(2(x+1)))/(x-1)\\\\((-4(x-1))/(2(x+1)))/(x-1)\\\\(-4)/(2(x+1))\\ \\(-2)/((x+1))`