Question

HELP!!! FAN AND MEDAL!!!!!

Answer 1

\[\frac{ x-3 }{ x }+\frac{ 3 }{x ^{2} +x }=\frac{ 3 }{ x+1 }\]
Solve.

Answer 2

Factor the 2nd denominator.
Now - what's the LCD? Multiply both sides of the equation by that, and *poof* all the fractions will disappear.
Then you should have a quadratic equation to solve - either by factoring (if possible) or quadratic formula (if not).
Be sure to check for extraneous solutions!

Answer 3

Is the LCD x?

Answer 4

No - remember that the LCD has to be a MULTIPLE of ALL the denominators. And x+1 is not a multiple of x.

Did you factor the 2nd denominator? What do you get? You HAVE to see all the factors before you can determine the LCD.

Answer 5

I got x(x+1)

Answer 6

ok, good. So your denominators are:
x
x+1
x(x+1)

So what's the LCD?

Answer 7

I'm not sure, x+1?

Answer 8

No, because x is not a multiple of (x+1). The LCD has to be a multiple of the all the denominators, just like with numbers.

I have to be able to take each denominator, and multiply it by SOMETHING (possibly 1) and GET the LCD. I need an LCD so that:

x(?)=LCD
(x+1)(?)=LCD
x(x+1)(?)=LCD

Remember, the (?) might be 1, but there has to be SOME PRODUCT with each denominator that gets me to the LCD.

Answer 9

In other words, there is nothing I can put in for the "?" so that:

x(?)=x+1
or
(x+1)(?)=x

So neither of those (alone) are the LCD.

Answer 10

so then i would have to multiply by x(x+1)?

Answer 11

So would i like multiply the first fraction by (x+1) and the last by x?

Answer 12

so they would all be x(x+1)?

Answer 13

Right! Your LCD is x(x+1). Multiply both sides of the equation by that. In the first term, left side, x's cancel so you get (x-3)(x+1). In 2nd term, left side, the whole denominator cancels with LCD. On right side, x+1 cancels so you get 3x.

Now take the FOIL product of the binomials, gather all terms on left side to set =0. You have a quadratic equation. Solve using quadratic equation methods.

Answer 14

So would my work be:
(x-3)(x+1)+3=3x
then
x^2+x-3x-3+3=3x
then
x^2-2x=3x
then
x^2-5x=0?

Answer 15

@DebbieG

Answer 16

never mind i made silly mistake

Answer 17

:(

Answer 18

help.....

Answer 19

haha i got it, never mind :)

Answer 20

Sorry, I missed the notifications above. Glad you got it! :)

Answer 21

thanks for being so patient with me :) sorry it took me a long time to understand xD

Answer 22

I understand it now :D