Need a problem checked on solving a rational equation

[Violagirl]

Hi, I just wanted to have my problem checked. Did I do this right?

Solve the following equation:

1/2+8/x=4+1/x


2x(1/2+8/x)=2x(4+1/x)

= 1+16x=8x+2

16x=8x+1

8x=1

x=1/8?

If not, what did I do wrong?

 

[stapel]

Solve the following equation: 1/2+8/x=4+1/x

As posted, the equation is as follows:

. . . . .\(\displaystyle \frac{1}{2}\, +\, \frac{8}{x}\, =\, 4\, +\, \frac{1}{x}\)

Was this what you meant? (Your solution cannot be verified until the equation is known.)

Note: The solution to any "solving" problem may be checked by plugging the answer back into the original exercise. What do you get when you plug "1/8" in for "x"?

Thank you!

Eliz.

 

[Violagirl]

I got really wierd fractions on both sides. On the left I got 8/7 and the other I got 6/5 so it must not be right. Thanks for the tip!


I have just one more question.

On this problem:

x/(x-2)=1+1/(X-9)

I know I have to find the common denominator on both sides so it'd be (x-2) and (x-9. On the right side for the single digit 1, would it mulitply into both quantities or just (x-2)?

 

[stapel]

On this problem: x/(x-2)=1+1/(X-9)

I know I have to find the common denominator on both sides so it'd be (x-2) and (x-9. On the right side for the single digit 1, would it mulitply into both quantities or just (x-2)?

I'm not sure what you're saying here...?

I will guess that the equation is as follows:

. . . . .\(\displaystyle \frac{x}{x\, -\, 2}\, =\, 1\, +\, \frac{1}{x\, -\, 9}\)

In particular, I will guess that you mean "x" and "X" to be, contrary to standard practice, actually the same variable.

I think you are multiplying through by the common denominator, (x - 2)(x - 9), as:

. . . . .\(\displaystyle \left(\frac{(x\, -\, 2)(x\, -\, 9)}{1}\right)\, \left(\frac{x}{x\, -\, 2}\right)\, =\, \left(\frac{(x\, -\, 2)(x\, -\, 9)}{1}\right)\, \left(\frac{1}{1}\right)\, +\, \left(\frac{(x\, -\, 2)(x\, -\, 9)}{1}\right)\, \left(\frac{1}{x\, -\, 9}\right)\)

...leading to:

. . . . .\(\displaystyle \left(\frac{(x\, -\, 9)}{1}\right)\, \left(\frac{x}{1}\right)\, =\, (x\, -\, 2)(x\, -\, 9)\, +\, \left(\frac{(x\, -\, 2)}{1}\right)\, \left(\frac{1}{1}\right)\)

. . . . .\(\displaystyle x(x\, -\, 9)\, =\, (x\, -\, 2)(x\, -\, 9)\, +\, (x\, -\, 2)\)

But I'm afraid I don't understand what you're saying after that...?

Please reply with clarification, showing your work and reasoning. Thank you!

Eliz.

 

[Violagirl]

That's exactly what I was trying to say, thank you! After foiling everything out, I got

x^2-9x=x^2-10x+16 after combining everything. After I combine these numbers, I get x=16 but it doesn't factor out right when I check it. I'm clueless as to what I've been doing wrong.

 

[Deleted member 4993]

That's exactly what I was trying to say, thank you! After foiling everything out, I got

x^2-9x=x^2-10x+16 after combining everything. After I combine these numbers,

I get x=16 <<< This is correct


but it doesn't factor out right <<< What do you mean - please show work


when I check it. I'm clueless as to what I've been doing wrong.