SOLUTION: Please help me answer this equation: x/9-8/x=1/9

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Question 195568This question is from textbook McDougal Littell Algebra 1
: Please help me answer this equation: x/9-8/x=1/9 This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2F9-8%2Fx=1%2F9 Start with the given equation.


Multiply every term on both sides by the LCD 9x. Doing this will eliminate all of the fractions.


x%28x%29-9%288%29=x%281%29 Cancel out and simplify


x%5E2-72=x Multiply


x%5E2-72-x=0 Subtract x from both sides.


x%5E2-x-72=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc=0 where a=1, b=-1, and c=-72


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=-72


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--288+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-72%29 to get -288


x+=+%281+%2B-+sqrt%28+1%2B288+%29%29%2F%282%281%29%29 Rewrite sqrt%281--288%29 as sqrt%281%2B288%29


x+=+%281+%2B-+sqrt%28+289+%29%29%2F%282%281%29%29 Add 1 to 288 to get 289


x+=+%281+%2B-+sqrt%28+289+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+17%29%2F%282%29 Take the square root of 289 to get 17.


x+=+%281+%2B+17%29%2F%282%29 or x+=+%281+-+17%29%2F%282%29 Break up the expression.


x+=+%2818%29%2F%282%29 or x+=++%28-16%29%2F%282%29 Combine like terms.


x+=+9 or x+=+-8 Simplify.


So the answers are x+=+9 or x+=+-8