Question

For the rational equation 6x+5/x^2+2x+2=6x-7/x^2-2x+2, do each of the following:

a. using successive approximations, find an approximate solution on the interval [-2,-1] such that the difference between the two sides of the equation is less than 0.1. your answer should be the midpoint of an interval.

b. state the interval for which the solution is a midpoint

c. show that the difference of the two sides of the equation is less than 0.1 for this value of x.

Answer 1

you want the difference to be small, so start checking
(6x+5)/(x^2+2x+2) - (6x-7)/(x^2-2x+2)
y = -4(3x^2-x-6)/(x^4+1)
Since the denominator is always positive, you want to find an interval containing a zero of
f(x) = 3x^2-x-6
f(-2) = 14
f(-1) = -2
So now find y(1.5) and keep subdividing the interval till you get |y| < 0.1

Answer 2

Thank you so much for the help!