Find the values of the variable y, for which

Question

the sum of the fractions 6/y+1 and y/y−2 is equal to their product

the sum of the fractions 

6

y+1

 and 

y

y−2

 is equal to their product

Answer 1

The way to type these in line is to use parentheses:

6/(y+1) + y/(y-2) = 6/(y+1) • y/(y-2)

The common denominator for the addition is:

(y-1)(y+2)

6(y-2)/(y-2)(y+1) + y(y+1)/(y-2)(y+1) = 6y/(y-2)(y+1)

These denominators are all the same.

Multiply both sides by (y-2)(y+1).

6(y-2) + y(y+1) = 6y

6y-12 + y²+y = 6y

y²+y-12=0

(y-3)(y+4) = 0

y = 3, -4