SOLUTION: On the following I always get a no solutions answer, but its noted that their are real solutions in this problem. Can you help me? Find all real solutions of the equation. (Roun

Algebra ->  Equations -> SOLUTION: On the following I always get a no solutions answer, but its noted that their are real solutions in this problem. Can you help me? Find all real solutions of the equation. (Roun      Log On


   

Question 196634: On the following I always get a no solutions answer, but its noted that their are real solutions in this problem. Can you help me?
Find all real solutions of the equation. (Round your answer to two decimal places. If there are extra answer boxes, enter NONE in the last boxes.)
3 / (x - 3) + 6 / (x^2) = 0

thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3+%2F+%28x+-+3%29+%2B+6+%2F+%28x%5E2%29+=+0 Start with the given equation.


Multiply EVERY term by the LCD x%5E2%28x-3%29 to clear out the fractions.


x%5E2%283%29%2B%28x-3%29%286%29=0 Multiply and simplify


3x%5E2%2B6%28x-3%29=0 Rearrange the terms.


3x%5E2%2B6x-18=0 Distribute


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=3, B=6, and C=-18


Let's use the quadratic formula to solve for x


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%283%29%28-18%29+%29%29%2F%282%283%29%29 Plug in A=3, B=6, and C=-18


x+=+%28-6+%2B-+sqrt%28+36-4%283%29%28-18%29+%29%29%2F%282%283%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36--216+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-18%29 to get -216


x+=+%28-6+%2B-+sqrt%28+36%2B216+%29%29%2F%282%283%29%29 Rewrite sqrt%2836--216%29 as sqrt%2836%2B216%29


x+=+%28-6+%2B-+sqrt%28+252+%29%29%2F%282%283%29%29 Add 36 to 216 to get 252


x+=+%28-6+%2B-+sqrt%28+252+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-6+%2B-+6%2Asqrt%287%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%286%29+%2B-+%286%2Asqrt%287%29%29%2F%286%29 Break up the fraction.


x+=+-1+%2B-+sqrt%287%29 Reduce.


x+=+-1%2Bsqrt%287%29 or x+=+-1-sqrt%287%29 Break up the expression.


So the solutions are x+=+-1%2Bsqrt%287%29 or x+=+-1-sqrt%287%29


which approximate to x=1.646 or x=-3.646