Solving Rational equations. LCD method. Show work. Image attached. (m)/(m+1) + (5)/(m-1) = 1

Question

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


`(m)/(m+1) + (5)/(m-1) = 1`

Answer 1

`m=-(3)/(2)`

Explanation:

The given equation is

`(m)/(m+1)+(5)/(m-1)=1`

The Least Common Denominator is
`(m-1)(m+1)`.

We multiply through by the LCD to get;

`(m-1)(m+1)* (m)/(m+1)+(m-1)(m+1)*(5)/(m-1)=(m-1)(m+1)*1`

Simplify

`(m-1)* (m)/(1)+(1)(m+1)*(5)/(1)=(m-1)(m+1)*1`

`m(m-1)+5(m+1)=(m-1)(m+1)`

Expand;(Use difference of two squares on the right hand side)

`m^2-m+5m+5=m^2-1`

Group similar terms;

`m^2-m^2-m+5m=-1-5`

Simplify;

`4m=-6`

Divide through by 4.

`m=(-6)/(4)`

`m=-(3)/(2)`