What is (7x-x^2)/(x^2-49) ?

The solution to (7x-x^2)/(x^2-49) is -x/(x+7)

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simplify (7x-x^2)/(x^2-49)

simplify

\frac{7 x - x ^{2}}{x ^{2} - 49}

- \frac{x}{x + 7}

Solution steps

\frac{7 x - x ^{2}}{x ^{2} - 49}

Factor

7 x - x^{2} : x (7 - x)

= \frac{x ( 7 - x )}{x ^{2} - 49}

Factor

x^{2} - 49 : (x + 7) (x - 7)

= \frac{x ( 7 - x )}{( x + 7 ) ( x - 7 )}

x (7 - x) = - x (x - 7)

= \frac{- x ( x - 7 )}{( x + 7 ) ( x - 7 )}

Cancel the common factor:

x - 7

= \frac{- x}{x + 7}

Apply the fraction rule:

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

= - \frac{x}{x + 7}

- 576

\frac{1}{5} (- 10 + - 125)

(3 + 2 i) (4 - 5 i)

35 + 75 - 10

(3 p^{3} q)^{\frac{3}{4}}