Algebra 2

[greatwhiteshark]

Simplify:

5/(x^2 - 3x) + 3/(3 - x) = 3/x

MY WORK:

1) factor the left side denominator

5/x(x-3) + 3/3-x = 3/x

Here's where I get stuck:

How do I convert 3-x on the right side denominator to equal the left side denominator, which is x - 3? Or is 3-x the same as x - 3????

 

[Denis]

Simplify:

5/(x^2 - 3x) + 3/(3 - x) = 3/x

MY WORK:

1) factor the left side denominator

5/x(x-3) + 3/3-x = 3/x

Here's where I get stuck:

How do I convert 3-x on the right side denominator to equal the left side denominator, which is x - 3? Or is 3-x the same as x - 3????

The "left side denominator" is NOT x-3: it's x(x-3)

3-x is NOT same as x-3; let x=5: 3-5=-2 and 5-3=2
So x-3 = -1(3-x); so 2nd term becomes -3/(x-3)

So equation becomes:
5/(x^2 - 3x) - 3/(x - 3) = 3/x

5 / x(x-3) = 3/x + 3 / (x-3) : easier if 2nd term is switched to right side'

5 / x(x-3) = [3(x-3) + 3x] / x(x-3)

5 = 3(x-3) + 3x : cancel out denominators, since they're the same

5 = 3x - 9 + 3x

6x = 14

x = 14/6 = 7/3

That's not an easy one, Janet; hope you can follow what I did;
perhaps someone else will make it clearer...anyway, x = 7/3 is correct.

 

[soroban]

Hello, greatwhiteshark!

Solve: 5/(x^2 - 3x) + 3/(3 - x) = 3/x

You're thinking along the right track . . .
There is a relationshp between the three denominators.

You factored the first denominator correctly: . x² - 3x .= .x(x - 3)

Here's the "trick"
. . . Factor -1 out of the second denominator: . 3 - x .= .-1(x - 3)

. . . . . . . . . . . . . . . .5 . . . . . 3 . . . . . 3
So it becomes: . --------- - ------ . = . --
. . . . . . . . . . . . . x(x - 3) . .x - 3 . . . . x

Can you finish it now?

 

[greatwhiteshark]

yes...

I can complete the question from this point on.
My problem was converting 3-x to x-3. I now multiply all fractions by the LCD and simplify.