SOLUTION: My math book says that (2a^2 + 11a - 6)/(a^2 + 6a) = (2a - 1)/(a). I don't understand this. What happened to the 11? Why is there still an "a" on each side? I would appreciate

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: My math book says that (2a^2 + 11a - 6)/(a^2 + 6a) = (2a - 1)/(a). I don't understand this. What happened to the 11? Why is there still an "a" on each side? I would appreciate       Log On


   

Question 1023325: My math book says that (2a^2 + 11a - 6)/(a^2 + 6a) = (2a - 1)/(a). I don't understand this. What happened to the 11? Why is there still an "a" on each side? I would appreciate it if you would explain it to me. Thanks!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
start with:

%282a%5E2+%2B+11a+-+6%29%2F%28a%5E2+%2B+6a%29

factor the numerator and the denominator and you will get:

%28%28a%2B6%29%2A%282a-1%29%29+%2F+%28a%2A%28a%2B6%29%29

the (a+6) in the numerator and the denominator cancel out and you are left with:

%282a-1%29+%2F+a

if you don't know how to factor a quadratic, then check out the following tutorial which should be helpful.

http://www.purplemath.com/modules/factquad.htm

if you had used the quadratic formula, which is the method of last resort for factoring a quadratic equation, then you would have gotten:

a = -6 or a = 1/2.

to find the factors from this, you would do the following:

solve each equation for 0.

from a = -6, add 6 to both sides to get a + 6 = 0.

from a = 1/2, subtract 1/2 from both sides to get a - 1/2 = 0.

multiply both sides by 2 to get 2a - 1 = 0.

your factors are (a + 6) and (2a - 1).

the quadratic formula assumes the variable is x.

your variable is a.

change your variable name to x to use the formula and then change the result back to a variable name of a.

the formula will tell you that x = -6.

just make this a = -6 and you get your answer in terms of a.