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Solve the equation.`4/(3x^2+16x +5) - 2/(x^2 +3x -10) =0`

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seerboldly | Student, Grade 10 | (Level 1) Salutatorian

Posted April 25, 2013 at 1:19 PM via iOS

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Solve the equation.`4/(3x^2+16x +5) - 2/(x^2 +3x -10) =0`

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted April 25, 2013 at 1:46 PM (Answer #1)

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`4/(3x^2 +16x +5) - 2/(x^2 +3x -10) =0`

First you need to simplify the denominators so as to create a common denominator or LCD. Use the factors of the first term and the third term to determine the brackets:

`3x^2 +16x +5 = (x+5)(3x+1)`

`and x^2 +3x -10 = (x+5)(x-2)`

`therefore` LCD = `(x+5)(3x+1)(x-2)`

Now apply this to your equation:

`(4(x-2) - 2(3x+1))/((x+5)(3x+1)(x-2)) = 0`

Now you can operate without the denominator and simplify:

`4x - 8 - 6x - 2 = 0`

Note the negative symbols

`therefore 4x-6x - 10 = 0`

`therefore -2x = 10`

`therefore x=10/(-2)` 

`therefore x = -5`

Ans x=-5

 

 

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