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Exercise

$\frac{4x\sin\left(2x\right)}{\sin^2\left(5x\right)}$

Step-by-step Solution

1

Since $\sin$ is the reciprocal of $\csc$, $\frac{4x\sin\left(2x\right)}{\sin\left(5x\right)^2}$ is equivalent to $4x\csc\left(5x\right)^2\sin\left(2x\right)$

$4x\csc\left(5x\right)^2\sin\left(2x\right)$

Final answer to the exercise

$4x\csc\left(5x\right)^2\sin\left(2x\right)$

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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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