SOLUTION: Hey, I'm needing some help checking this problem for an exam review: Solve the equation: (5/a) - (7)/(a+1) = (a^2 - 2a + 4)/(a^2 + a) thanks!

Algebra ->  Equations -> SOLUTION: Hey, I'm needing some help checking this problem for an exam review: Solve the equation: (5/a) - (7)/(a+1) = (a^2 - 2a + 4)/(a^2 + a) thanks!      Log On


   

Question 190424: Hey, I'm needing some help checking this problem for an exam review:
Solve the equation:
(5/a) - (7)/(a+1) = (a^2 - 2a + 4)/(a^2 + a)
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%5E2+%2B+a%29+ Start with the given equation.


5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%28a+%2B+1%29%29+ Factor the last denominator


So we can see that the LCD is a%28a%2B1%29. Take note that a%3C%3E0 or a%3C%3E-1 (these values cause a division by zero)


Multiply EVERY term by the LCD a%28a%2B1%29 to clear the fractions


5%28a%2B1%29-7a=a%5E2+-+2a+%2B+4 Simplify


5a%2B5-7a=a%5E2+-+2a+%2B+4 Distribute


5-2a=a%5E2+-+2a+%2B+4 Combine like terms.


0=a%5E2+-+2a+%2B+4-5%2B2a Get all of the terms to the right side.


0=a%5E2+-+1 Combine like terms.


0=%28a%2B1%29%28a-1%29 Factor


a%2B1=0 or a-1=0 Set each factor equal to zero


a=-1 or a=1 Solve each equation


Remember, our original restrictions are a%3C%3E0 or a%3C%3E-1. So this means that a=-1 is NOT a solution


So the only solution is a=1