using rational functions solve (x+5)/(x-3)= (2x+7)/(x)

Question

thank you

Answer 1

as with all fractions , cross-multiply to get rid of them:

(x+5)(x) = (2x+7)(x-3) assuming x≠0,3
x^2+5x = 2x^2+x-21
x^2-4x-21 = 0
(x-7)(x+3) = 0
x = -3,7

check:
(-3+5)/(-3-3) = -1/3 = (-6+7)/(-3)
(7+5)/(7-3) = 3 = (14+7)/7