How do you simplify $\frac{7 x + 14}{7 x^{2} - 7 x - 42}$ $(7x+14)/(7x^2-7x-42)$ ?

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Answer 1 · 2018-03-27T07:31:11

$\frac{1}{x - 3}$ $color(blue)(1/(x-3))$

$\frac{7 x + 14}{7 x^{2} - 7 x - 42}$ $(7x+14)/(7x^2-7x-42)$

Factor out 7 from numerator and denominator:

$\frac{7 (x + 2)}{7 (x^{2} - x - 6)}$ $(7(x+2))/(7(x^2-x-6))$

Cancel:

$(cancel(7)(x+2))/(cancel(7)(x^2-x-6))=((x+2))/((x^2-x-6))$

Factor denominator:

$((x+2))/((x+2)(x-3))$

Cancel:

$(cancel((x+2)))/(cancel((x+2))(x-3))=color(blue)(1/(x-3))$

This result could also be achieved by factoring the denominator at the beginning, but this is a bit more difficult than factoring in stages:

How do you simplify (7x+14)/(7x^2-7x-42)7x+147x2−7x−42(7x+14)/(7x^2-7x-42)?