What is (2-x)/(x^2+4x-12) ?

The solution to (2-x)/(x^2+4x-12) is -1/(x+6)

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simplify (2-x)/(x^2+4x-12)

simplify

\frac{2 - x}{x ^{2} + 4 x - 12}

- \frac{1}{x + 6}

Solution steps

\frac{2 - x}{x ^{2} + 4 x - 12}

Factor

x^{2} + 4 x - 12 : (x - 2) (x + 6)

= \frac{2 - x}{( x - 2 ) ( x + 6 )}

2 - x = - (x - 2)

= \frac{- ( x - 2 )}{( x - 2 ) ( x + 6 )}

Cancel the common factor:

x - 2

= \frac{- 1}{x + 6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{x + 6}

\frac{41}{3} \div \frac{22}{5}

\frac{\frac{x}{x + 1}}{\frac{x}{x + 1} + 1}

- 24 x - 6 x^{5}

\frac{3}{5} - \frac{4}{5}

\frac{1}{3 + 7}