What is factor (5x^8-20x^4)/(5x^8+20x^6+20x^4) ?

The solution to factor (5x^8-20x^4)/(5x^8+20x^6+20x^4) is (x^2-2)/(x^2+2)

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factor (5x^8-20x^4)/(5x^8+20x^6+20x^4)

factor

\frac{5 x ^{8} - 20 x ^{4}}{5 x ^{8} + 20 x ^{6} + 20 x ^{4}}

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

Solution steps

\frac{5 x ^{8} - 20 x ^{4}}{5 x ^{8} + 20 x ^{6} + 20 x ^{4}}

Factor

5 x^{8} - 20 x^{4} : 5 x^{4} (x^{4} - 4)

= \frac{5 x ^{4} ( x ^{4} - 4 )}{5 x ^{8} + 20 x ^{6} + 20 x ^{4}}

Factor

5 x^{8} + 20 x^{6} + 20 x^{4} : 5 x^{4} (x^{4} + 4 x^{2} + 4)

= \frac{5 x ^{4} ( x ^{4} - 4 )}{5 x ^{4} ( x ^{4} + 4 x ^{2} + 4 )}

Cancel

\frac{5 x ^{4} ( x ^{4} - 4 )}{5 x ^{4} ( x ^{4} + 4 x ^{2} + 4 )} : \frac{x ^{4} - 4}{x ^{4} + 4 x ^{2} + 4}

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x^{2} + 2

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

8 < 2 (a + 3) < 10

x^{2} + 3 x + 5 < 5

\frac{1}{1 - x} \leq \frac{3}{x}

(6^{5})^{4}

\frac{25}{x} < x

What is factor (5x^8-20x^4)/(5x^8+20x^6+20x^4) ?
The solution to factor (5x^8-20x^4)/(5x^8+20x^6+20x^4) is (x^2-2)/(x^2+2)