[tex]4.a) \frac{2-3x}{x^{2}-1} + \frac{2}{ x -1}+ \frac{5}{3x} \\ \\ =\frac{2-3}{ x(x-1)}+ \frac{2}{ x -1}+ \frac{5}{3x} \\ \\ 3(2-3x)+2\cdot2\cdotx+5(x-1)=0 \\ \\ 6-9x+6x+5x-5=0 \\ \\ x=- \frac{1}{2} [/tex]
[tex]4.c) \frac{2x-5}{3x-1} - \frac{2x+3}{3x+1}+ \frac{2x+8}{9 x^{2} -1} \\ \\ (2x-5)(3x+1)-(2x+3)(3x-1)+2x+8 \\ \\ 6 x^{2} +2x-15x-5-(6 x^{2} -2x+9x-3)+2x+8= \\ \\ -13x=6 \\ \\ x=- \frac{6}{13} [/tex]
[tex]6.a) \frac{4}{x+2}- \frac{x+10}{ x^{2} -4}+ \frac{3}{x-2}= \\ \\ 4(x-2)- (x+10)+3(x+2)= \\ \\ =4x-8-x-10+3x+6 \\ \\ 6x-12=0 \\ \\ 6x=12 \\ \\ x=2[/tex]
[tex]7.c)\frac{x+1}{x-1}+ \frac{4}{ x^{2} -1}+ \frac{1-x}{x+1}= \\ \\ (x+1)^{2} +4+(1-x)(x-1)= \\ \\ = x^{2} +2x+1+4+x-1-x+x \\ \\ x^{2} +3x+4=0 \\ \\ x1=-2;x2=-1[/tex]
