SOLUTION: 1+3/x=5/x^2

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Question 186688: 1+3/x=5/x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2B3%2Fx=5%2Fx%5E2 Start with the given equation.


x%5E2%2B3x=5 Multiply EVERY term by the LCD x%5E2 to clear out the fractions.


x%5E2%2B3x-5=0 Subtract 5 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=3, and c=-5


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-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Plug in a=1, b=3, and c=-5


x+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--20+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-5%29 to get -20


x+=+%28-3+%2B-+sqrt%28+9%2B20+%29%29%2F%282%281%29%29 Rewrite sqrt%289--20%29 as sqrt%289%2B20%29


x+=+%28-3+%2B-+sqrt%28+29+%29%29%2F%282%281%29%29 Add 9 to 20 to get 29


x+=+%28-3+%2B-+sqrt%28+29+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-3%2Bsqrt%2829%29%29%2F%282%29 or x+=+%28-3-sqrt%2829%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%28-3%2Bsqrt%2829%29%29%2F%282%29 or x+=+%28-3-sqrt%2829%29%29%2F%282%29


which approximate to x=1.193 or x=-4.193