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# 4/3x=10/3+3/x ⚑ Flag

by emmanuel032 at December 06, 2009

rational equation

## Answers

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

thatsJim December 07, 2009

I'm not sure if your equation is supposed to be (4/3)x = 10/3 + 3/x, or 4/(3x) = 10/3 + 3/x.  I'll solve for x for you with the first version.(4/3)x = 10/3 + 3/x  (*3x on each side to get rid of fractions)4x = 10x + 9  (subtract 10x to the other side)-6x = 9  (divide by -6 to get x alone.)x = -9/6 = -3/2

Alison037 December 07, 2009

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

Alison037 December 07, 2009

if you multiply it all by 3, you get 4x=10+9/x then you multiply by x and get 4x^2=10x+90=-4x^2+10x+9then use the quadratic formula

DoggiLov December 08, 2009

Because you are asking about rational equations, I read this asâ€¦  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, itâ€™s just a simple equationâ€¦ 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 doesnâ€™t. Valid solution, check!

bpeters December 16, 2009

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