What is (x^2-4x)/(16-x^2) ?

The solution to (x^2-4x)/(16-x^2) is -x/(4+x)

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simplify (x^2-4x)/(16-x^2)

simplify

\frac{x ^{2} - 4 x}{16 - x ^{2}}

- \frac{x}{4 + x}

Solution steps

\frac{x ^{2} - 4 x}{16 - x ^{2}}

Factor

x^{2} - 4 x : x (x - 4)

= \frac{x ( x - 4 )}{16 - x ^{2}}

Factor

16 - x^{2} : (4 + x) (4 - x)

= \frac{x ( x - 4 )}{( 4 + x ) ( 4 - x )}

(4 + x) (4 - x) = - (4 + x) (x - 4)

= \frac{x ( x - 4 )}{- ( 4 + x ) ( x - 4 )}

Cancel the common factor:

x - 4

= \frac{x}{- ( 4 + x )}

Apply the fraction rule:

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

= - \frac{x}{4 + x}

32 + 550

(2 a^{2} + 3 b) (2 a^{2} - 3 b)

\frac{x ^{3} - 27 y ^{3}}{x ^{2} - 9 y ^{2}}

x - (- 2 x + 4)

∣ 1 - 1 ∣