SOLUTION: solving for x 7x+3 over x squared-8x+15 + 3x over x-5 = 1 over 3-x how would I rearrange the (3-x) so that the x won't be a negative? if I factor out a -1, does that mean tha

Algebra ->  Rational-functions -> SOLUTION: solving for x 7x+3 over x squared-8x+15 + 3x over x-5 = 1 over 3-x how would I rearrange the (3-x) so that the x won't be a negative? if I factor out a -1, does that mean tha      Log On


   

Question 287168: solving for x
7x+3 over x squared-8x+15 + 3x over x-5 = 1 over 3-x
how would I rearrange the (3-x) so that the x won't be a negative? if I factor out a -1, does that mean that I do it to the WHOLE probem? or just the fraction of 1/3-x ?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(7x+3)/(x^2-8x+15)+3x/(x-5)=1/(3-x)
%287x%2B3%29%2F%28x%5E2-8x%2B15%29%2B3x%2F%28x-5%29=1%2F%283-x%29
%287x%2B3%29%2F%28%28x-3%29%2A%28x-5%29%29%2B3x%2F%28x-5%29=1%2F%283-x%29

Multiply the whole equation by the denominator
%287x%2B3%29%2B%283x%2A%28x-3%29%29=-%281%2A%28x-5%29%29
7x%2B3%2B3x%5E2-9x=5-x
3x^2-2x+3=5-x
3x^2-x-2=0
(x-1)*(3 x+2) = 0
x=1
3x+2=0
3x=-2
x=-2/3
x=1
x=(1,-2/3)