Rational equations

Question

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

1. Solve the rational equation using a calculator. Graph the left side of the equation as y1 and the right sides as y2. Enter your solution(s):

2.Explain how you used the graph to find the solutions using complete sentences.

please answer both questions

Answer 1

When solving an equation using graphing, the way we are looking at it is considering the left and right-hand-side as two different functions. The equals sign is asking "at which x-values are these two functions the same?" which amounts to looking for the graphs intersect each other! It's a pretty cool idea.

So in your situation, we consider one function

y1 = (2x+2/x-1)-4

and the other function

y2 = (6x/x+4)

Now if you graph these as separate functions, you will see two separate graphs. Then, you can find any locations where the two graphs intersect. The x-coordinates of these intersection points are the solutions to the equation!