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

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

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Answer 1 · 2018-06-08T08:21:22

$\frac{1}{x - 2}$ $1/(x-2)$

Explanation:

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

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

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

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

Re-write the equation as follows:

$x^{2} - 5 x + 6$ $x^2-5x+6$

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

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

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

So now we have;

$\frac{x - 3}{x^{2} - 5 x + 6}$ $(x-3)/(x^2-5x+6)$ = $\frac{x - 3}{(x - 2) (x - 3)}$ $(x-3)/((x-2)(x-3))$ = $cancel(x-3)/((x-2)cancel((x-3))$ = $1/(x-2)$

Hence its simplified as:

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

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

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