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

The solution to (cos(x)-2)/(cos^2(x)-4) is 1/(cos(x)+2)

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

simplify

\frac{cos ( x ) - 2}{cos ^{2} ( x ) - 4}

\frac{1}{cos ( x ) + 2}

Solution steps

\frac{cos ( x ) - 2}{cos ^{2} ( x ) - 4}

Factor

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

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

Cancel the common factor:

cos (x) - 2

= \frac{1}{cos ( x ) + 2}

\frac{18 w ^{\frac{1}{3}} v ^{\frac{5}{4}}}{27 w ^{\frac{4}{3}} v ^{\frac{1}{2}}}

\frac{9 x ^{2}}{3 x + 1} - \frac{1}{3 x + 1}

5 x^{3} - 9 x^{2} + 28 x + 6

(x - 1) (2 x - 1)

\frac{4 x ^{2} - 1}{4 x ^{2} + 4 x + 1}

What is (cos(x)-2)/(cos^2(x)-4) ?
The solution to (cos(x)-2)/(cos^2(x)-4) is 1/(cos(x)+2)