Math CentralQuandaries & Queries


Question from Kenssa, a parent:

Simplify: 3-(7/x)-(6/x^2) / (3/x^2)+(5/x)-2

Hi Kenssa,

The problem as I read it is to simplify

\[\frac{3 - \frac7{x} - \frac6{x^2}}{\frac3{x^2} + \frac5{x} - 2}\]

I would begin by multiplying the numerator and the denominator by $x^2$. This will result in a fraction which is equivalent to the one in your problem. Let me focus on the numerator

\[3 - \frac7{x} - \frac6{x^2}.\]

multiplying by $x^2$ this becomes

\[3x^2 - 7x - 6.\]

This is a quadratic that you can factor.

Apply the same procedure to the denominator, put the fraction back together and simplify.


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