How do you simplify the rational expression: (x-3)/(x^2-5x+6)#?

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Answer 1 · 2018-06-08T08:21:22

$1/(x-2)$

Simply the $x^2-5x+6$ first:

Lets find the factors of $x^2-5x+6$

$3 xx 2 = 6$ ----> adding them gives $5$ ----> we want adding it gives $-5$

$-3 xx -2 = 6$ ----> adding them gives $-5$ ---> This is the one.

Re-write the equation as follows:

$x^2-5x+6$

$x^2-3x-2x + 6$

$x(x-3)-2(x-3)$

$(x-2)(x-3)$

So now we have;

$(x-3)/(x^2-5x+6)$ = $(x-3)/((x-2)(x-3))$ = $cancel(x-3)/((x-2)cancel((x-3))$ = $1/(x-2)$

Hence its simplified as:

$(x-3)/(x^2-5x+6)$ = $1/(x-2)$