[tex]\frac{2x-3}{8} -\frac{3x-2}{4} =\frac{x+1}{2}\,|\cdot8[/tex]
[tex]8(\frac{2x-3}{8} -\frac{3x-2}{4} )=8\cdot\frac{x+1}{2}[/tex]
[tex]\frac{8(2x-3)}{8} ^{(8}-\frac{8(3x-2)}{4} ^{(4}=\frac{8(x+1)}{2} ^{(2}[/tex]
[tex]2x-3-2(3x-2)=4(x+1)[/tex]
[tex]2x-3-6x+4=4x+4[/tex]
[tex]2x-3-6x+4-4=4x[/tex]
[tex]2x-3-6x=4x[/tex]
[tex]2x-6x-3=4x[/tex]
[tex]-4x-3=4x\implies -4x=4x+3[/tex]
[tex]\implies -4x-4x=3\implies-8x=3\implies x=-\frac{3}{8}[/tex]
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[tex]\frac{x+3}{2} +\frac{x-2}{4} =\frac{5}{6} \,|\cdot12[/tex]
[tex]12(\frac{x+3}{2} +\frac{x-2}{4} )=12\cdot\frac{5}{6}[/tex]
[tex]\frac{12(x+3)}{2}^{(2} +\frac{12(x-2)}{4}^{(4} =\frac{12\cdot5}{6} ^{(6}[/tex]
[tex]6(x+3)+3(x-2)=2\cdot5[/tex]
[tex]6x+18+3x-6=10[/tex]
[tex]9x+18-6=10[/tex]
[tex]9x+12=10 \,|-12 \implies 9x=-2\implies x=-\frac{2}{9}[/tex]
