Question

solve for x:
x/(x=3)+ 5/(x-7) =30/x^2-4x-21

Answer 1

Alright let's get them all to have the same denominator and you'll get :\[[x(x-7) + 5(x+3) -30]/(x-7)(x+3)\]

now let's simplify and do the calculation:
\[[x^2-7x +5x + 15 -30]/(x+3)(x-7)\]
\[(x^2-2x-15)/(x+3)(x-7)\]
\[(x+3)(x-5)/(x-7)(x+3)\]
(x-5)/(x-7)

hmm, I think you can take over from here :) good luck!

Answer 2

I question the x/(x=3) as shown in your original question. I to will assume it was meant to be a +. However the next equal sign I will take at face value and what you have is;\[x/(x+3)+5/(x-7)= 30/(x ^{2}-4x-21)\]

Note that the denominators of both fractions are equivalent and the two fractions are equal.
It can now be said the x+5 =30 x can be solved: x=25