Find all values of y

S

samwertz3

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May 10, 2009
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Another problem type I am stumped on. If someone could take a look and see where I am going wrong, I would appreciate the help.

Find all values of y satisfying the equation

4 + 3/y-3 = - 5/y-4

so I find a common denom

4(y-3)(y-4) + 3(y-3)(y-4)/y-3 = - 5(y-4)(y-3)/y-4

gives me 4(y-3)(y-4) + 3(y-4) = - 5(y-3)

4y^2-25y+36=-5y+15

4y^2-20y-21

and this is where I am stuck. Maybe it is just really late and I cannot see how to factor this or maybe I did something wrong somewhere else...
 


Firstly, we must type parentheses around numerators and denominators when they consist of more than one term or factor.

Properly typed, the given equation is:

4 + 3/(y - 3) = -5/(y - 4)

You almost ended up with the correct quadratic equation:

4y^2 - 20y + 21 = 0

(Thirty-six minus fifteen is positive twenty-one.)

A*C = (4)(21) = 84

We're looking for two integers whose product is 84 and whose sum is -20.

The prime factorization of 84 is 2*2*3*7.

Hmmm. 2*7 = 14 and 2*3 = 6 and 14 + 6 = 20. It appears that the two integers are -14 and -6.

Rewrite the first-degree term in the quadratic polynomial.

4y^2 - 14y - 6y + 21 = 0

Can you now factor by grouping?

 
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