Question

Please help me out!! Solve the equation. y-6/y=5 A.y=1,5 B.y=-9,1 C.y=2,3 D.y=-1,6

Answer 1

Answer: y = -1, y = 6 (choice D)

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Work Shown:

y - (6/y) = 5
y*(y - (6/y)) = y*5 <<--- see note 1 below
y^2 - 6 = 5y
y^2 - 5y - 6 = 0
(y+1)(y-6) = 0 <<--- see note 2 below
y+1 = 0 or y-6 = 0
y = -1 or y = 6 which are the two answers

note 1: I multiplied both sides by y to clear out the fraction (the LCD is y)

note 2: I factored the left side by asking myself "what two numbers multiply to -6 and add to +5?" the answer to that question is +1 and -6 which helps lead to the factorization. An alternative route instead factoring is to use the quadratic formula

Answer 2

The answer is y₁=-1,y₂=6
because you have to determine the defined range
and move constant to left and change its sing