SOLUTION: Please help me solve this equation: 2+ 8/x-5=x+5/x^2-25

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Question 195562This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: 2+ 8/x-5=x+5/x^2-25 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!
2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28x%5E2-25%29 Start with the given equation.


2%2B8%2F%28x-5%29=%28x%2B5%29%2F%28%28x-5%29%28x%2B5%29%29 Factor. Take note that x%3C%3E-5 or x%3C%3E5 (these values cause a division by zero)


Multiply every term on both sides by the LCD %28x-5%29%28x%2B5%29. Doing this will eliminate all of the fractions.


2%28x-5%29%28x%2B5%29%2B8%28x%2B5%29=x%2B5


2%28x%5E2-25%29%2B8%28x%2B5%29=x%2B5 FOIL


2x%5E2-50%2B8x%2B40=x%2B5 Distribute


2x%5E2-50%2B8x%2B40-x-5=0 Get all terms to the left side.


2x%5E2%2B7x-15=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=7, and c=-15


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-%287%29+%2B-+sqrt%28+%287%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Plug in a=2, b=7, and c=-15


x+=+%28-7+%2B-+sqrt%28+49-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-15%29 to get -120


x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%282%29%29 Rewrite sqrt%2849--120%29 as sqrt%2849%2B120%29


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%282%29%29 Add 49 to 120 to get 169


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-7+%2B-+13%29%2F%284%29 Take the square root of 169 to get 13.


x+=+%28-7+%2B+13%29%2F%284%29 or x+=+%28-7+-+13%29%2F%284%29 Break up the expression.


x+=+%286%29%2F%284%29 or x+=++%28-20%29%2F%284%29 Combine like terms.


x+=+3%2F2 or x+=+-5 Simplify.


So the possible answers are x+=+3%2F2 or x+=+-5


However, recall that we stated earlier that x%3C%3E-5 (since it causes a division by zero). So x=-5 is NOT a solution.


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Answer:


So the only solution is x+=+3%2F2