What is (x^4-256)/(x-4) ?

The solution to (x^4-256)/(x-4) is (x^2+16)(x+4)

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simplify (x^4-256)/(x-4)

simplify

\frac{x ^{4} - 256}{x - 4}

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

Solution steps

\frac{x ^{4} - 256}{x - 4}

Apply exponent rules

= \frac{( x ^{2} ) ^{2} - 1 6 ^{2}}{x - 4}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2})^{2} - 1 6^{2} = (x^{2} + 16) (x^{2} - 16)

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

Factor

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

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

Cancel the common factor:

x - 4

= (x^{2} + 16) (x + 4)

- 6 - 2

\frac{5}{6 x} + \frac{3}{4 x}

\frac{6}{7} - \frac{4}{7}

\frac{45}{125}

43 + 3