# What is the coordinates of the point of intersection of the curve #y=1/(x+2) +3# and the line #y=-x#?

Those two curves do not intersect.

So we want to solve:

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.

graph{(y+x)(y-1/(x+2)-3)=0 [-17.02, 15.01, -5.2, 10.82]}

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The coordinates of the point of intersection of the curve ( y = \frac{1}{x+2} + 3 ) and the line ( y = -x ) are (-1, 1).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- A triangle has corners at #(4 ,3 )#, #(2 ,6 )#, and #(1 ,5 )#. How far is the triangle's centroid from the origin?
- For line #ST#, the coordinates of point #T# are T(0,4). The midpoint of ST is (5, -8). What are the coordinates of point #S#?
- Circle A has a center at #(2 ,4 )# and a radius of #9 #. Circle B has a center at #(1 ,-5 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
- A line passes through #(4 ,9 )# and #(8 ,7 )#. A second line passes through #(2 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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