Question

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

Answer 1

Answer:

$m=-\frac{3}{2}$

Step-by-step explanation:

The given equation is

$\frac{m}{m+1}+\frac{5}{m-1}=1$

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

We multiply through by the LCD to get;

$(m-1)(m+1)\times \frac{m}{m+1}+(m-1)(m+1)\times\frac{5}{m-1}=(m-1)(m+1)\times1$

Simplify

$(m-1)\times \frac{m}{1}+(1)(m+1)\times\frac{5}{1}=(m-1)(m+1)\times1$

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

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.

$m=\frac{-6}{4}$

$m=-\frac{3}{2}$