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

First we need to determine the common denominator and rewrite the equation:

common denominator is: (m+1)(m-1)

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

==> m(m-1) + 5(m+1)](m+1)(m-1) = 1

Now open brackets:

==? [m^2 - m + 5m + 5]/(m^2 -1)

==> (m^2 + 4m + 5) /(m^2-1) = 1

Now multiply both sides by (m^2 -1) :

==> m^2 + 4m + 5 = m^2 -1

Reduce similar:

==> 4m + 5= -1

Now subtract 5:

==> 4m = -6

divide by 4:

==> m = -6/4 = -3/2

==> m = -3/2

We notice that:

(m + 1)(m - 1) = m^1 -1

Therefore we can simplify the given equation by multiplying every term by m^2 - 1. Thus:

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

==> (m^2 - 1)[m/(m + 1)] + (m^2 - 1)[5/(m - 1)] = m^2 - 1

==> m(m - 1) + 5(m + 1) = m^2 - 1

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

==> m^2 + 4m + 5 = m^2 - 1

Taking all the terms containing m on left hand side, and other terms on right hand side:

==> m^2 - m^2 + 4m = - 5 - 1

==> 4m = - 6

Therefore:

m = -6/4 = -3/2 = -1.5

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

To solve for m.

Solution:

The denominators m+1 and m-1 could be got rid off by multiplying both sides by the LCM (or (m+1)(m-1) )of the denominators.

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

(m -1)m + 5(m+1) = m^2-1

m^2-m +5m+5 = m^2-1. Simplify both sides:

m^2+4m +5 = m^2-1. Subtract m^2 from both sides:

m^2+4m+5 - m^2 = m^2-1-m^2. m^2 and -m^2 cancells in each side.

4m+5 = -1. Subtract 5 from both sides:

-4m+5-5 = -1-5

4m = -6. Divide both sides by 4.

4m/4 = -6/4

m = -6/4 = -1.5

m = -1.5.