Question

How do you solve r+6/r-5=0 6/r is a fraction.

Answer 1

multiply both sides of the equation by r
\[ r(r+\frac{6}{r} -5)= 0 \cdot r \]
you get
\[ r^2 +6 -5r = 0 \]
or, arranging in descending powers
\[ r^2 -5r + 6 =0 \]
This is a quadratic equation. In this case we can factor it:
(r-2)(r-3) =0

so either r= 2 or r= 3

check:
\[ 2 +\frac{6}{2} - 5 = 2+3-5= 5-5= 0 \]
\[ 3 +\frac{6}{3} -5 = 3+2-5= 5-5= 0 \]