# Help with this math question!? Relevance

This tests if you understand that the intersection of the two graphs gives the solutions for both x and y. By sight that is  x = 2, y = 3.

In case the graph does not guarantee enough acccuracy you can confirm that result by substitution.

When x = 2, f(x) = 3 and h(x) = 3, so the intersection was at (2, 3)

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• If two equations are plotted as graph, the intersection is the solution.

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• from looking at the picture alone,

you know the solution is somewhere near (2,3)

check it first

f(2) = (2+1) / (2-1) = 3

h(2) = (2-2)^2  + 3  = 3

so the picture told you the answer.

You don't even have to do the algebra  (2,3)

if you did the algebra, it is little more complicated

(x+1)/(x-1) = (x-2)^2 +3

multiply both side by  (x-1)

(x+1)= (x-2)^2(x-1) + 3(x-1)x

x+1  = (x^2 -4x + 4)(x-1) + 3x -1

x+1  = x^3 -4x^2 + 4x -x^2 +4x -4 -1 +3x

x^3  -5x^2 + 10x -6 = 0

rational roots theorem says possible answers

are  +/-1 , +/- 2 , +/- 3 , and +/- 6

check shows

x =2 is the only solution

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• " f(x) = h(x)? " is simply just asking where both functions are equal to each other, or in other words where they meet at the same coordinate. You can see clearly on this graph that your answer as an ordered pair is (2, 3) .

It doesn't look like they're requiring it but you can also solve this mathematically by setting the two functions equal to each other and solving for x:

(x + 1)/(x - 1) = (x - 2)² + 3

This would be your initial set-up.

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