Question

simplify the rational expression.
\\(\frac{x^2 - 8x + 16}{x^2 - 12x + 32}\\)
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simplify the rational expression.
\\(\frac{9c^2 - 12c + 4}{3c^2 + 7c - 6}\\)

Explanation:

Step1: Factor numerator (1st expr)

$x^2-8x+16=(x-4)^2$

Step2: Factor denominator (1st expr)

$x^2-12x+32=(x-4)(x-8)$

Step3: Cancel common factors (1st expr)

$\frac{(x-4)^2}{(x-4)(x-8)}=\frac{x-4}{x-8}$

Step4: Factor numerator (2nd expr)

$9c^2-12c+4=(3c-2)^2$

Step5: Factor denominator (2nd expr)

$3c^2+7c-6=(3c-2)(3c+6)$

Step6: Cancel common factors (2nd expr)

$\frac{(3c-2)^2}{(3c-2)(3c+6)}=\frac{3c-2}{3c+6}$

Answer:

1. $\frac{x-4}{x-8}$ (where $x

eq 4, 8$)

1. $\frac{3c-2}{3c+6}$ (where $c

eq \frac{2}{3}, -2$)