((3a)/(a^2-b^2))- (4/(b-a))

(3a) / ( a² - b² )  -  4 / (b - a)

 

Find a common denominator by first factoring  a² - b²   --->   (a + b)(a - b)

 

The problem now is:  (3a) / [ (a + b)(a - b) ]  -  4 / (b - a)

 

Since the first term has  a - b  in the denominator while the second term has  b - a  in the denominator, change

b - a  into  -(a - b), so the problem now is:   (3a) / [ (a + b)(a - b) ]  -  4 / [ -(a - b) ]

 

Change   -  4 / [ -(a - b) ]   into   + 4 / (a - b)

 

The problem has become:  (3a) / [ (a + b)(a - b) ]  +  4 / (a - b)

 

To get a common denominator for both terms, multiply the second term by  (a + b) / (a + b):

--->     (3a) / [ (a + b)(a - b) ]  +  4(a + b)  / [ (a - b)(a + b) ]

 

Combining both fractions using the common denominator, it now is:   [ 3a + 4(a + b) ] / [ (a - b)(a + b) ]

--->     [ 3a + 4a + 4b ] / [ (a - b)(a + b) ]     --->     [ 7a + 4b ] / [ (a - b)(a + b) ]