SOLUTION: 3/x +3 = 3/4x + 25/8

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Question 152495: 3/x +3 = 3/4x + 25/8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283%29%2F%28x%2B3%29=%283%29%2F%284x%29%2B%2825%29%2F%288%29 Start with the given equation.


Multiply every term on both sides by the LCD 8x%28x%2B3%29. Doing this will eliminate all of the fractions.


24x=6%28x%2B3%29%2B25x%28x%2B3%29 Simplify


24x=6x%2B18%2B25x%5E2%2B75x Distribute


24x=6x%2B18%2B25x%5E2%2B75x Start with the given equation.


0=-24x%2B6x%2B18%2B25x%5E2%2B75x Get all terms to the left side.


0=25x%5E2%2B57x%2B18 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=25, b=57, 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-%2857%29+%2B-+sqrt%28+%2857%29%5E2-4%2825%29%2818%29+%29%29%2F%282%2825%29%29 Plug in a=25, b=57, and c=18


x+=+%28-57+%2B-+sqrt%28+3249-4%2825%29%2818%29+%29%29%2F%282%2825%29%29 Square 57 to get 3249.


x+=+%28-57+%2B-+sqrt%28+3249-1800+%29%29%2F%282%2825%29%29 Multiply 4%2825%29%2818%29 to get 1800


x+=+%28-57+%2B-+sqrt%28+1449+%29%29%2F%282%2825%29%29 Subtract 1800 from 3249 to get 1449


x+=+%28-57+%2B-+sqrt%28+1449+%29%29%2F%2850%29 Multiply 2 and 25 to get 50.


x+=+%28-57+%2B-+3%2Asqrt%28161%29%29%2F%2850%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-57%2B3%2Asqrt%28161%29%29%2F%2850%29 or x+=+%28-57-3%2Asqrt%28161%29%29%2F%2850%29 Break up the expression.


So our answers are x+=+%28-57%2B3%2Asqrt%28161%29%29%2F%2850%29 or x+=+%28-57-3%2Asqrt%28161%29%29%2F%2850%29


which approximate to x=-0.379 or x=-1.901