What is the least common denominator of the fraction 4 over x plus the fraction 2 x over x minus 1 plus the fraction x plus 3 over 2 x

2x (x-1)

Step-by-step explanation:

We have to find the least common denominator of the fraction

Least common denominator is the expression which should be divisible by all the denominators.

so, factors of x =  1. (x)

     factors of (x-1) = 1. ( x-1 )

    factors of 2x = 2. (x)

Therefore, expression which will be divisible by all denominators will be  

= 2(x) (x-1)

= 2x (x-1)

2x (x-1) will be the least common denominator.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).