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]
