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podryga [215]
3 years ago
5

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

Mathematics
1 answer:
kenny6666 [7]3 years ago
6 0

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}

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