What is (x^{n+2}+x^{n-2})/(x^{n-4)+x^n} ?

The solution to (x^{n+2}+x^{n-2})/(x^{n-4)+x^n} is x^2

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simplify (x^{n+2}+x^{n-2})/(x^{n-4)+x^n}

simplify

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

x^{2}

Solution steps

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

Factor out common term

x^{n - 2} : x^{n - 2} (x^{4} + 1)

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

Factor out common term

x^{n - 4} : x^{n - 4} (1 + x^{4})

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

Simplify

\frac{x ^{n - 2}}{x ^{n - 4}} : x^{2}

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

Apply the commutative law:

1 + x^{4} = x^{4} + 1

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

Cancel the common factor:

x^{4} + 1

= x^{2}

x^{2} - x^{5}

\frac{4}{4 x + 5} - \frac{4}{4 x - 5}

lo g_{16} (128)

80 - 45 - 20

\frac{4}{\frac{5}{4}}

What is (x^{n+2}+x^{n-2})/(x^{n-4)+x^n} ?
The solution to (x^{n+2}+x^{n-2})/(x^{n-4)+x^n} is x^2