What is domain of equation in x and solve 3/x+2-x-4/x^2+2x=1/3x?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to determine what x values work for the fractions to be defined such that:

`x+2 != 0 =gt x!=-2`

`x^2+2x != 0 =gt x(x+2) != 0 =gt x!=0 ; x!=-2`

`` `3x!=0 =gt x!=0`

Hence, the solutions to the equation need to be different of the values -2; 0.

You need to bring the fractions to a common denominator such that:

`9(x+2) - 3x + 12 = x + 2`

Opening the brackets yields:

`9x + 18 - 3x + 12 = x + 2`

`` You need to move the terms containing x to the left side, hence, you need to subtract x both sides such that:

`9x - 3x - x + 30 = 2`

`5x = 2 - 30 =gt 5x = 2 - 30 =gt 5x = -28 =gt x = -28/5`

Hence, the solution to the equation may be considered since is neither -2, nor 0, hence x = `-28/5` .

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