#1. (3/x) + (2/x+5) = (8/3x)
#2. (9/x+7) + (3x/x^2 +4x-21) + (8/x-3)
Thanks again for everyone's help!!
For #1, get a common denominator on the left side by multiplying the bottom of each fraction by the top of the other fraction:
$\displaystyle \frac{3(x+5) + 2(x)}{x(x+5)} = \frac{8}{3x}$
Distribute your terms in the top and bottom. Then cross multiply with the right side. Collect like terms...Can you go from there?
For #2, factor the denominator of the middle term, you should get (x+7)(x-3) then you should know what to do from there.
Good luck!
As currently formatted, the above mean the following:
. . . . .$\displaystyle \mbox{1. }\, \frac{3}{x}\, +\, \left(\frac{2}{x}\, +\, 5\right)\, =\, \frac{8}{3x}$
. . . . .$\displaystyle \mbox{2. }\, \left(\frac{9}{x}\, +\, 7\right)\, +\, \left(\frac{3x}{x^2}\, +\, 4x\, -\, 21\right)\, +\, \left(\frac{8}{x}\, -\, 3\right)$
However, I suspect that you mean the following:
. . . . .$\displaystyle \mbox{1. }\, \frac{3}{x}\, +\, \frac{2}{x\, +\, 5}\, =\, \frac{8}{3x}$
. . . . .$\displaystyle \mbox{2. }\, \frac{9}{x\, +\, 7}\, +\, \frac{3x}{x^2\, +\, 4x\, -\, 21}\, +\, \frac{8}{x\, -\, 3}$
Please confirm or correct. When you reply, please provide a clear listing of the progress you've made so far in solving these rational equations, so we can "see" where you're having trouble.
Thank you!