SOLUTION: this topic is Solving Rational Equations and our teacher wanted us to provide a solution for 6/y + 19/5 = y and i got confused. pls help

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Question 981690: this topic is Solving Rational Equations and our teacher wanted us to provide a solution for 6/y + 19/5 = y
and i got confused. pls help

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest common denominator is 5y, so multiply left and right members by it. This is basic fraction skills.

5y%286%2Fy%2B19%2F5%29=5y%28y%29

30%2B19y=5y%5E2

5y%5E2-19y-30=0, general form quadratic equation.
Maybe you could factor, maybe not.

Formula for general solution of a quadratic equation: First find discriminant.
%28-19%29%5E2-4%2A5%2A%28-30%29
19%5E2%2B20%2A30
19%5E2%2B600
961
highlight_green%2831%5E2%29, the discriminant.

y=%2810%2B-+31%29%2F%282%2A5%29

highlight%28y=-21%2F10%29 or highlight%28y=41%2F10%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
this topic is Solving Rational Equations and our teacher wanted us to provide a solution for 6/y + 19/5 = y
and i got confused. pls help
6%2Fy+%2B+19%2F5+=+y, with y+%3C%3E+0

30+%2B+19y+=+5y%5E2 ------- Multiplying by LCD, 5y

5y%5E2+-+19y+-+30+=+0

(5y + 6)(y - 5) = 0

5y + 6 = 0          OR          y - 5 = 0

y+=+%28-+6%2F5%29           OR          y = 5

highlight_green%28system%28y+=+-+1.2or%2Cy+=+5%29%29