Consider the rational equation 1/r=(1/x)+(1/y).find the value of r when x=2/5 and y=3/4.

R =  

Step-by-step explanation:

Given the rational equation as:

To find:

The value of R when x =

and, y =

now,

substituting the given values of x and y in the given rational equation,

or

⇒

or

⇒

or

⇒

or

⇒

now on rearranging, we get

⇒ R =  

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

the answer

b. they are parallel and will never intersect.