You can put this solution on YOUR website! x+6/x+5=x+4/x-3----(1)
Mulltiplying by (x+5)(x-3) (which is the lcm of (x+5) and (x-3) )
(x+6)(x-3) = (x+4)(x+5)
x(x-3)+6(x-3) = x(x+5)+4(x+5)
x^2-3x+6x-18 = x^2+5x+4x+20
x^2+3x-18 = x^2+9x+20
(x^2-x^2) +(3x-9x) -18-20 = 0 (grouping like terms)
0-6x-38 =0
-6x = 38
x = 38/(-6) = -19/3
Answer: x =-19/3
Verification: x= -19/3 in (1)
LHS = [(-19/3)+6]/[(-19/3)+5] = [(-19+18)/3]/[(-19+15)/3]= (-1)/(-4) = 1/4
RHS = [(-19/3)+4]/[(-19/3)-3] = [(-19+12)/3]/[(-19-9)/3]= (-7)/(-28) = 1/4=LHS
Therefore our answer is correct
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