a)$\frac{7x-3}{x-1}$ = $\frac{2}{3}$
⇔ 3(7x -3) = 2(x - 1)
⇔ 21x -9 = 2x-2
⇔ 21x -2x = -2 +9
⇔ 19x = 7
⇔ x = $\frac{7}{19}$
b) $\frac{2(3-7x)}{1+x}$ = $\frac{1}{2}$
⇔$\frac{6-14x}{1+x}$ = $\frac{1}{2}$
⇔2(6-14x) = 1+x
⇔ 12-28x-1-x =0
⇔11-29x = 0
⇔-29x = 11
⇔ x = $\frac{11}{29}$
c)$\frac{x+1}{x-1}$ - $\frac{x-1}{x+1}$ = $\frac{4}{x^{2} }$
⇔$\frac{x+1}{x-1}$(x-1)(x+1)- $\frac{x-1}{x+1}$(x-1)(x+1)= $\frac{4}{x^{2}-1}$ (x-1)(x+1)
⇔(x+1)²-(x-1)² =4
⇔x²+2x+1+(-x²)+2x-1=4
⇔4x =4
⇔x =1
d)$\frac{8-x}{x-7}$ -8 = $\frac{1}{x-7}$
⇔8-x-8(x-7)=1
⇔8-x-8x+56=1
⇔-x-8x=1-8-56
⇔-9x = -63
⇔ x= 7