i need this question answered please. solve for x

Question

(x-5/x-7)+1=x-6/x-5

Answer 1

Multiply through by (x-7)(x-5): (x-5)^2+(x-7)(x-5)=(x-6)(x-7). Expanding: x^2-10x+25+x^2-12x+35=x^2-13x+42. Gather together similar terms: x^2-9x+18=0, so (x-3)(x-6)=0 and x=3 or 6. Put these values in the original equation to check the result: (-2/-4)+1=3/2=(-3/-2). Correct! (1/-1)+1=0=(0/1). Correct!