Solve the equations and check for extraneous solutions

2.  ... I think this is   x/10= (x+1)/(2x-2) - (1)/(x-1) =

And getting a common denominator on the right, we have

x/10= (x+1)/(2(x-1)) - (2)/(2(x-1))   =  

x/10  = (x -1)/(2(x- 1))     cross multiply

x(2(x-1) = 10(x - 1)    simplify

2x^2 - 2x  = 10x - 10   simplify, again

2x^2 - 12x + 10 = 0      divide everything by 2

x^2 - 6x + 5 = 0     factor

(x - 5) ( x - 1)  = 0      and setting both factors to 0, we have that x = 5 or x = 1

We have to reject the second answer since it makes a denominator in the original problem = 0

1. I suspect this might be .... ( x-1)/(x-5) = (2x+7)/x     cross-multiply....

x(x - 1)  = (x - 5)(2x + 7)

x^2 - x  = 2x^2 - 3x - 35    rearrange

x^2 - 2x - 35 = 0     factor

(x -7) ( x + 5) = 0      and setting both factors to 0, we have that  x = 7 or x = -5.....both solutions are good