SOLUTION: Solve 3x-1/4x+7 = 1 - 6/x+7

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Question 167713: Solve
3x-1/4x+7 = 1 - 6/x+7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283x-1%29%2F%284x%2B7%29=1-%286%29%2F%28x%2B7%29 Start with the given equation.


Multiply EVERY term on both sides by the LCD %284x%2B7%29%28x%2B7%29. Doing this will eliminate all of the fractions.



%28x%2B7%29%283x-1%29=%284x%2B7%29%28x%2B7%29-6%284x%2B7%29 Multiply and simplify


3x%5E2%2B20x-7=4x%5E2%2B35x%2B49-6%284x%2B7%29 FOIL


3x%5E2%2B20x-7=4x%5E2%2B35x%2B49-24x-42 Distribute


3x%5E2%2B20x-7=4x%5E2%2B11x%2B7 Combine like terms.


3x%5E2%2B20x-7-4x%5E2-11x-7=0 Get all terms to the left side.


-x%5E2%2B9x-14=0 Combine like terms.


-%28x%5E2-9x%2B14%29=0 Factor a -1 from the left side


x%5E2-9x%2B14=0 Divide both sides by -1



Now here are two ways to solve this:


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Method # 1: Factoring


x%5E2-9x%2B14=0 Start with the given equation

%28x-7%29%28x-2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-7=0 or x-2=0

x=7 or x=2 Now solve for x in each case


So our answers are

x=7 or x=2



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Method # 2 Quadratic Formula


x%5E2-9x%2B14=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-9, and c=14


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-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%2814%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-9, and c=14


x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%2814%29+%29%29%2F%282%281%29%29 Negate -9 to get 9.


x+=+%289+%2B-+sqrt%28+81-4%281%29%2814%29+%29%29%2F%282%281%29%29 Square -9 to get 81.


x+=+%289+%2B-+sqrt%28+81-56+%29%29%2F%282%281%29%29 Multiply 4%281%29%2814%29 to get 56


x+=+%289+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 56 from 81 to get 25


x+=+%289+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%289+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


x+=+%289+%2B+5%29%2F%282%29 or x+=+%289+-+5%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+7 or x+=+2 Simplify.


So the answers are x+=+7 or x+=+2



Either way, you get the same answers.