Solve the equation

Question

3/m-2+ 1/m-1 = 7/ m²-3m+2

Answer 1

The first step in this type of problem is to factor everything you can. The only expression you can factor is m² - 3m + 2 = (m - 2)(m - 1). That makes the equation:

 

3 / (m - 2) + 1 / (m - 1) = 7 / ((m - 2)(m - 1))

 

Now, let's get rid of the denominators by multiplying both sides by every factor that appears there. Start with multiplying by (m - 2):

 

(m - 2) (3 / (m - 2) + 1 / (m - 1)) = (m - 2) (7 / ((m - 2)(m - 1)))

(3(m - 2)) / (m - 2) + (1(m - 2)) / (m - 1) = (7(m - 2)) / ((m - 2)(m - 1))

3 / 1 + (m - 2) / (m - 1) = 7 / (m - 1)

3 + (m - 2) / (m - 1) = 7 / (m - 1)

 

Next, let's multiply by (m - 1):

 

(m - 1) (3 + (m - 2) / (m - 1)) = (m - 1) (7 / (m - 1))

3(m - 1) + ((m - 1)(m - 2) / (m - 1)) = (7(m - 1) / (m - 1))

3m - 3 + ((m - 2) / 1) = 7 / 1

3m - 3 + (m - 2) = 7

3m - 3 + m - 2 = 7

 

Finally, combine like terms and solve for m:

 

4m - 5 = 7

4m = 12

m = 3