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Exercise

$\frac{-tan^{2\left(x\right)-1}}{sec^2\left(x\right)}$

Step-by-step Solution

1

Since $\sec$ is the reciprocal of $\cos$, $\frac{-\tan\left(x\right)^{\left(2x-1\right)}}{\sec\left(x\right)^2}$ is equivalent to $-\cos\left(x\right)^2\tan\left(x\right)^{\left(2x-1\right)}$

$-\cos\left(x\right)^2\tan\left(x\right)^{\left(2x-1\right)}$

Final answer to the exercise

$-\cos\left(x\right)^2\tan\left(x\right)^{\left(2x-1\right)}$

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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