Simplify completely quantity 4 x squared minus 7 x plus 3 all over x squared plus 5 x minus 6

First, I'm going to write out the expression to make it easier to simplify. This expression is (4x^2 - 7x + 3)/(x^2 + 5x - 6). Now, we must factor both trinomials. Using the bottoms up method and the quadratic equation ((-b +/- sqrt(b^2 - 4ac))/2a), we can get an expression of ((x - 1)(4x - 3))/((x - 1)(x + 6)). Finally, we can cancel out the (x - 1) in the numerator with the (x - 1) in the denominator. This gives us a final expression of (4x - 3)/(x + 6).

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