Question

Solve: ((3)/(x^(2)-3x))-(8)/(x)=(4)/(x-3)

Answer 1

x=9/4

Answer 2

when solving rational (fractional) equations, multiply by the LCD=x(x-3) to clear denominators\[x(x-3)*\frac{3}{x(x-3)}-x(x-3)*\frac{8}{x}=\frac{4}{x-3}*x(x-3)\]\[3-8(x-3)=4x\]now solve the polynomial you just created\[3-8x+24-4x=0\]\[-8x=-27\]\[x=\frac{27}{12}=\frac{9}{4}\]in general, when solving rational equations you should "check" your solution(s) at a point before you multiplied by the LCD to see if the equation is satisfied; in this problem that means the original equation

in this case x=9/4 does satisfy the original equation and so the solution set is\[\left\{ \frac{9}{4} \right\}\]
Note: if you want/ned to see the "check" just make it a separate post and someone will go through the steps for you