. . .(10/x) - (12/x - 3) + 4 = 0

The "10/x" and "12/x-3" are fractions.

Looking at it, the answer appears to be 5, but I'm having a hard time getting it. Could someone point me in the right direction? Thank you!

- Thread starter Guitarman
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. . .(10/x) - (12/x - 3) + 4 = 0

The "10/x" and "12/x-3" are fractions.

Looking at it, the answer appears to be 5, but I'm having a hard time getting it. Could someone point me in the right direction? Thank you!

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- Feb 4, 2004

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So you mean the equation to be as follows?Guitarman said:The "10/x" and "12/x-3" are fractions.

. . . . .10/x - 12/(x - 3) + 4 = 0

I'm sorry, but what do you mean "looking at it"? Do you mean that you're looking at the equation and trying to solve it in your head, without pencil or paper...?Guitarman said:Looking at it, the answer appears to be 5....

A good first step for solving rational equations is to multiply through by the common denominator. Then solve the resulting equation. (In this case, it will be a simple quadratic equation. So there could be two solutions.)

Eliz.

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You can check the solution to any "solving" problem by plugging your answer back into the original question. In this case:Guitarman said:ok after I did all that I get x=3 or x=3.5. seems right to me

. . .x = 3:

. . . . .10/[3] - 12/([3] - 3) ...

No; 3 - 3 = 0, and division by zero is not defined. So "x = 3" cannot be a solution. Continuing:

. . .x = 3.5:

. . . . .10/[3.5] - 12/([3.5] - 3) + 4

. . . . .= 10/(35/10) - 12/0.5 + 4

. . . . .= (10/1)(10/35) - (12/1)(2/1) + 4

. . . . .= 100/35 - 24 + 4

. . . . .= 20/7 - 20

. . . . .= 20/7 - 140/7

. . . . .= -120/7

So "x = 3.5" cannot be a solution.

Please reply showing all of your steps. Thank you.

Eliz.