SOLUTION: solve each equations. indicate the lower comon demominator. 4+3/x+2=4/x^2+2x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve each equations. indicate the lower comon demominator. 4+3/x+2=4/x^2+2x       Log On


   

Question 165095: solve each equations. indicate the lower comon demominator.
4+3/x+2=4/x^2+2x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%2B3%2F%28x%2B2%29=4%2F%28x%5E2%2B2x%29 Start with the given equation


4%2B3%2F%28x%2B2%29=4%2F%28x%28x%2B2%29%29 Factor x%5E2%2B2x to get x%28x%2B2%29


So the LCD is x%28x%2B2%29


Multiply EVERY term by the LCD x%28x%2B2%29 to clear the fractions.


4x%28x%2B2%29%2B3x=4 Simplify.


4x%5E2%2B8x%2B3x=4 Distribute.


4x%5E2%2B8x%2B3x-4=0 Subtract 4 from both sides.


4x%5E2%2B11x-4=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=11, and c=-4


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-%2811%29+%2B-+sqrt%28+%2811%29%5E2-4%284%29%28-4%29+%29%29%2F%282%284%29%29 Plug in a=4, b=11, and c=-4


x+=+%28-11+%2B-+sqrt%28+121-4%284%29%28-4%29+%29%29%2F%282%284%29%29 Square 11 to get 121.


x+=+%28-11+%2B-+sqrt%28+121--64+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-4%29 to get -64


x+=+%28-11+%2B-+sqrt%28+121%2B64+%29%29%2F%282%284%29%29 Rewrite sqrt%28121--64%29 as sqrt%28121%2B64%29


x+=+%28-11+%2B-+sqrt%28+185+%29%29%2F%282%284%29%29 Add 121 to 64 to get 185


x+=+%28-11+%2B-+sqrt%28+185+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-11%2Bsqrt%28185%29%29%2F%288%29 or x+=+%28-11-sqrt%28185%29%29%2F%288%29 Break up the expression.


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Answer:


So the solutions are x+=+%28-11%2Bsqrt%28185%29%29%2F%288%29 or x+=+%28-11-sqrt%28185%29%29%2F%288%29


which approximate to x=0.325 or x=-3.075