4/3x=10/3+3/x

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4/3x = 10x+3(3)/3x4/3x=(10x+9)/3x30x^2+27x=12x30x^2+15x=0use quadratic formulaanswer:x=-0.5andx=o

Whoops, I forgot to multiply the x on the first side in the second step.(4/3)x = 10/3 + 3/x (*3x on each side to get rid of fractions)4x^2 = 10x + 94x^2 - 10x - 9 = 0Using quadratic formula, you get:x = 3.20256242 or x = -0.702562419If you do it as 4/(3x) = 10/3 + 3/x the answer is:4/(3x) = 10/3 + 3/x (*3x to get rid of fractions)4 = 10x + 9  (subtract 9 to the other side to get x term alone)-5 = 10x  (divide by 10 to get x alone)-(1/2) = x

Because you are asking about rational equations, I read this as…  4   =   10  +  3 ---       ----     ---- 3x        3        x   which greatly affects the answer.   Multiply everything by 3x to get the same denominator across the board.   4 = 10x + 9 Now, it’s just a simple equation… not quadratic.   Subtract 9 from both sides. -5 = 10x   Divide by 10. x = -5/10 = -1/2   Plug back into your original problem to make sure it will NOT make any denominator 0, which it doesn’t. Valid solution, check!