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Exercise

$\frac{1-\cos\left(4x\right)}{2x\sin\left(3x\right)}$

Step-by-step Solution

1

Use the trigonometric identity: $1-\cos\left(2x\right)=2\sin\left(x\right)^2$

$\frac{2\sin\left(2x\right)^2}{2x\sin\left(3x\right)}$
2

Simplify the fraction $\frac{2\sin\left(2x\right)^2}{2x\sin\left(3x\right)}$ by $2$

$\frac{\sin\left(2x\right)^2}{x\sin\left(3x\right)}$

Final answer to the exercise

$\frac{\sin\left(2x\right)^2}{x\sin\left(3x\right)}$

Try other ways to solve this exercise

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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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