x-6=(x^2/x+1)-2

Question

Solve the equation above graphically (explain how you do this) and algebraically. Your solution(s) should be rounded to the nearest hundredth for the graphical solution and presented as an exact value for the algebraic solution. (

Answer 1

x-6 = x^2/(x+1) -2

x-4= x^2/(x+1)

(x-4)(x+1) = x^2

x^2 -3x -4 = x^2

3x =-4

x=-4/3

check the answer

-4/3- 6 = (16/9)/(-4/3+1) -2

-22/3 = (16/9)/-1/3 -2

-22/3 = -16/3 -2 =(-16-6)/3 = -22/6

it works

graphically, graph the left side, it's an upward sloping line

then graph the right side, plot some points, connect them with a line

and see where the two lines intersect, at the point (-4/3, -22/3) quadrant 3