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Simplify the expression $\frac{\tan\left(x-\frac{\pi}{6}\right)}{6x-\pi }$

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Solution

Videos

Algebra 2 - Learn step by step how to simplify a complex fraction, (3/(x+1)) / (5/(x -1))

https://www.youtube.com/watch?v=uXVIkvfXzr8

Tutorial - Simplifying complex fractions ex 33, ((x/3) -6) / (10+(4/x))

https://www.youtube.com/watch?v=kIJ8S9gVJ6Q

Algebra 1 - Distributive Property, 4x(2x+y); -3(3a^2 -a+7); 2xy(x^2 -3xy+4x); (x/6)(x^2 +5x-9)

https://www.youtube.com/watch?v=4xx87GKdm04

Algebra 2 - Dividing two rational expressions (x^2/x^2 - y^2) / (4x/y-x)

https://www.youtube.com/watch?v=5MNXHwO_COA

Pre-Calculus - How to simplify a trig expression using co-function, sin((pi/2) -x)/cos((pi/2) -x)

https://www.youtube.com/watch?v=LxdYYK2mnx4

Algebra 2 Learn how to find the exact value of an angle using sum formula for tangent, tan(5(pi)/12)

https://www.youtube.com/watch?v=EIW9JHLvbkw

Derivative

$\frac{d}{dx}\left(\frac{\tan\left(x-\frac{\pi}{6}\right)}{6x-\pi }\right)=\frac{\left(6x-\pi \right)\sec\left(x-\frac{\pi}{6}\right)^2-6\tan\left(x-\frac{\pi}{6}\right)}{\left(6x-\pi \right)^2}$ See full solution

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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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