Simplify the difference. State and restrictions on the variable. X/3x+9 - 8/x^2+3x
To simplify the difference (X/3x + 9) - (8/x^2 + 3x), we need to find a common denominator for the fractions.
The LCD is 3x(x^2 + 3x).
(X/3x + 9) - (8/x^2 + 3x)
= (X*x^2 + 3x*X + 9*3x(x^2 + 3x))/(3x(x^2 + 3x)) - (8*3x + 3x(x^2 + 3x))/(3x(x^2 + 3x))
= (X*x^2 + 3x^2 + 27x^2 + 81x)/(3x(x^2 + 3x)) - (24x + 3x^3 + 9x)/(3x(x^2 + 3x))
= (4Xx^2 + 108x^2 + 81x)/(3x(x^2 + 3x)) - (24x + 3x^3 + 9x)/(3x(x^2 + 3x))
= (4Xx^2 + 108x^2 + 81x - 24x - 3x^3 - 9x)/(3x(x^2 + 3x))
= (-3Xx^2 + 75x^2 + 48x)/(3x(x^2 + 3x))
= (-3Xx + 75x + 48)/(x^2 + 3x)
There are no restrictions on the variable X.