<span>(x-2)/x + 3/20 = (x+1)/(x+3) </span> <span>times 20x(x+3) , the LCD </span> <span>20(x+3)(x+1) + 3x(x+3) = 20x(x+1) </span> <span>expanding and simplifying gave me </span> <span>x^2 + 3x - 40 = 0 </span> <span>(x-5)(x+8) = 0 </span> <span>x = 5 or x=-8 </span>
<span>if x=5, the original fraction was 3/5 </span> <span>if x=-8 the original fraction was -10/-8 or 5/4 </span>
<span>check for 3/5 , new fraction would be 6/8 or 3/4 </span> <span>3/5 + 3/20 = 12/20 + 3/20 = 15/20 = 3/4 </span>
<span>but for 5/4, new fraction would be 8/7 </span> <span>5/4 + 3/20 = 28/20 = 7/5 ≠ 8/7 </span> <span>BUT, if we take the unsimplified fraction -10/-8 , new fraction would be -7/-5 = 7/5 </span>
<span>So the original fraction would be 3/5 for sure, but </span> <span>also the unsimplified fraction -10/-8</span>
