What is (x^3-64)/(16-x^2) ?

The solution to (x^3-64)/(16-x^2) is -(x^2+4x+16)/(4+x)

Popular >

simplify (x^3-64)/(16-x^2)

simplify

\frac{x ^{3} - 64}{16 - x ^{2}}

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

Solution steps

\frac{x ^{3} - 64}{16 - x ^{2}}

Factor

x^{3} - 64 : (x - 4) (x^{2} + 4 x + 16)

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

Factor

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

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

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

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

Cancel the common factor:

x - 4

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

Apply the fraction rule:

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

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

- (x - 4)^{2}

\frac{x ^{5} - 3 x ^{2} + 2 x}{x}

lo g_{12} (87.5)

- x^{2} - 6 x - 7

\frac{2 a ^{2}}{3 b} \cdot \frac{6 b ^{2}}{4 a}

What is (x^3-64)/(16-x^2) ?
The solution to (x^3-64)/(16-x^2) is -(x^2+4x+16)/(4+x)