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