Question 173260: I need help with writing this in lowest terms
1. y^2+8y+12/y^2+9y+14
Simplify the complex fraction
2. x/x+1/9/x^2-1
Factoring to solve the equation
3. r^2+12r+36=14
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Whenever you are asked to simplify an expression with one or more quadratic expression in it (like all of these problems have), try factoring the quadratic expression.
1. Factor each quadratic polynomial separately.
y^2 + 8y + 12 = (y + 2)(y + 6)
y^2 + 9y + 14 = (y + 2)(y + 7)
So (y^2 + 8y + 12)/(y^2 + 9y + 14) = [(y + 2)(y + 6)]/[(y + 2)(y + 7)].
The (y + 2) in the numerator and denominator cancel out, so the fraction becomes (y + 6)/(y + 7). Since nothing else is factorable, this is the final answer.
2. Again, try to factor any quadratic expression. In this case, that's only (x^2 -1).
x^2 - 1 = (x + 1)(x - 1)
So [x/(x+1)]/[9/(x^2-1) = [x/(x+1)]/[9/(x+1)(x-1)] = [x/(x+1)] = x(x-1)/9
3. For this one, remember, you can factor something into (x-a)(x-b)=0, and then you will know x=a and x=b. So first you need this to look like ax^2+bx+c=0. So subtract 14 from each side to get r^2+12r+22=0. Actually, I am not sure if you wrote the correct numbers in the original equation, because this does not factor in any nice way. But if the equation was, for example, r^2+13r+36=14, you would subtract 14 to get r^2+13r+22=0. Then you would factor it into (r+2)(r+11)=0, so the solution would be r=-2,-11. Hopefully that will be mildly helpful. Best of luck!
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