Solving Rational equations. LCD method. Show work. Image attached. (2b-5)/(b-2) -2 = (3)/(b+2)

Question

Solving Rational equations. LCD method. Show work. Image attached.


`(2b-5)/(b-2) -2 = (3)/(b+2)`

Answer 1

`b=1`

Explanation:

The given rational equation is

`(2b-5)/(b-2) -2=(3)/(b+2)`

The Least Common Denominator is
`(b+2)(b-2)`.

Multiply each term in the equation by the LCD.

`(b+2)(b-2)* (2b-5)/(b-2) -(b+2)(b-2)*2=(b+2)(b-2)*(3)/(b+2)`

Simplify;

`(b+2)* (2b-5)/(1) -2(b+2)(b-2)=(b-2)*(3)/(1)`

`(b+2)(2b-5) -2(b+2)(b-2)=3(b-2)`

Expand and group similar terms

`2b^2-5b+4b-10 -2(b^2-4)=3b-6`

`2b^2-5b+4b-10 -2b^2+8=3b-6`

`-b-2=3b-6`

`3b+b=-2+6`

`4b=4`

`b=1`