Answer:[tex]b=1[/tex]Step-by-step explanation:The given rational equation is [tex]\frac{2b-5}{b-2} -2=\frac{3}{b+2}[/tex]The Least Common Denominator is [tex](b+2)(b-2)[/tex].Multiply each term in the equation by the LCD.[tex](b+2)(b-2)\times \frac{2b-5}{b-2} -(b+2)(b-2)\times2=(b+2)(b-2)\times\frac{3}{b+2}[/tex]Simplify;[tex](b+2)\times \frac{2b-5}{1} -2(b+2)(b-2)=(b-2)\times\frac{3}{1}[/tex][tex](b+2)(2b-5) -2(b+2)(b-2)=3(b-2)[/tex]Expand and group similar terms[tex]2b^2-5b+4b-10 -2(b^2-4)=3b-6[/tex][tex]2b^2-5b+4b-10 -2b^2+8=3b-6[/tex][tex]-b-2=3b-6[/tex][tex]3b+b=-2+6[/tex][tex]4b=4[/tex][tex]b=1[/tex]