I'm quite clueless as to how to solve this. I know the quadratic equation but am not sure how to get this equation into the format to plug in to the quadratic...

Question

Solve the quadratic equation using the formula [1/(1+x)]-[1/(3-x)]=(6/35)
Show your work

Answer 1

multiply both sides by 35(x+1)(x-3)

then
35(x-3)+35(x+1)=6(x-3)(x+1)

and you should be able to assemble it from there.

Answer 2

so should i just multiply that all out and then plug it in?

Answer 3

Write the two terms on the left with a common denomimnator. Then convert to standard quadratic form.

[(3-x) - (1+x)]/[(1+x)(3-x)] = 6/35
(2-2x)/[(1+x)(3-x)] = 6/35
(1-x) = (3/35)[(1+x)(3-x)]
35 -35x = 3[-x^2 +2x +3)
3x^2 -41x +26 = 0
(3x -2)(x-13)
Check my work. No guarantees

Answer 4

We were lucky that one factored fairly easily. x = 2/3 or 13

Answer 5

i got the same answer but used the quadratic :) thank you for all your help everyone!