# What are the solutions for the function : f(x) = (x^2 - 5x + 6) / (x -3)

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f(x) = (x^2 - 5x + 6) / (x-3)

To determine the solution of the function first we need to determine the points such that f(x) is defined.

we know that the function f(x) is not defined when the denominator is 0:

Then we will exclude x values where (x-3) = 0

==> x = 3

Then f(x) is defined for R- { 3}

Now we will calculate the roots.

The roots for f(x) is the roots for the numerator:

==> (x^2 - 5x + 6) = 0

We will factor:

==> ( x^2 - 5x + 6) = (x-2)(x-3) = 0

==> x = { 2, 3} are the roots

But f(x) is not defined when x = 3

**Then the only solution is x = 2**

To find the solutions of f(x) =( x^2-5x+6)/(x-3).

This is not an equation. So we can only simplify the given expression .

The numerator x^2-5x+6 could be factored. If we find a common factor to both numerator and denominator of the right side, then we can further reduce f(x) by dividing numerator and denominator by the common factor.

Cosider the numerator for factorising:

x^2-5x+6 = x^2-3x- 2x +6.

x^2-5x+6 = x(x-3) -2(x-3).

x^2-5x+6 = (x-3)(x-2).

Therefore f(x) = (x^2-5x+6)/(x-3) = (x-3)(x-2)/(x-3)

So f(x) = x-2 in simplified form.