What is the coordinates of the point of intersection of the curve #y=1/(x+2) +3# and the line #y=-x#?
1 Answer
Those two curves do not intersect.
Explanation:
To find an intersection we try to find an
So we want to solve:
We'll begin by clearing the fraction. Multiply both sides of the equation by
We see an
We try to solve by factoring, but we don't see how to factor this, so either solve by completing the square or solve using the quadratic formula.
But now we notice (if we didn't notice before) that
So there is no solution in the real numbers.
Therefore, there is no point of intersection for the curves.
Here is the graph. Of course,
graph{(y+x)(y-1/(x+2)-3)=0 [-17.02, 15.01, -5.2, 10.82]}