Solve the problem below, please

Question

2/(4y^2-9)+1/(2y-3)=3/(2y+3)

Answer 1

2/(4y²-9)+1/(2y-3)=3/(2y+3)  

 

Notice that (4y²-9) = (2y-3)(2y+3) so use (4y²-9) as the common denominator

 

= 2/(4y²-9) + (2y+3)/(4y²-9) = 3(2y-3)/(4y²-9)

 

Because all the denominators are common, set up an equation using just the numerators.

 

2 + 2y+3 = 6y-9

2y + 5 = 6y - 9

14 = 4y

14/4 = y

7/2 = y

 

Check:

2/(49-9) + 1/(7-3) = 3/(7+3)

2/40 + 1/4 = 3/10

1/20 + 5/20 = 6/20  check