Solve for y y+6/y=5

Problem

y+6/y=5

Solution

1. Multiply the entire equation by y to eliminate the fraction, assuming y≠0

y*(y+6/y)=5*y

2. Distribute y on the left side of the equation.

y2+6=5*y

3. Rearrange the equation into standard quadratic form a*y2+b*y+c=0 by subtracting 5*y from both sides.

y2−5*y+6=0

4. Factor the quadratic expression by finding two numbers that multiply to 6 and add to −5

(y−2)*(y−3)=0

5. Apply the zero product property to find the possible values for y

y−2=0⇒y=2

y−3=0⇒y=3

Final Answer

y=2,3

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