How do you simplify #(8n-3)/(n^2+8n+12)-(5n-9)/(n^2+8n+12)#?

Question

Eva Abramson · Accepted Answer

#(8n-3)/(n^2+8n+12)-(5n-9)/(n^2+8n+12)=3/(n+6)#

Let ,

#P=(8n-3)/(n^2+8n+12)-(5n-9)/(n^2+8n+12)#

#P=((8n-3)-(5n-9))/(n^2+8n+12)larr......... "Combine fractions"#

#P=(8n-3-5n+9)/(n^2+8n+12)#

#P=(3n+6)/(n^2+8n+12).......................................to(1)#

Now , we obtain factors:

#3n+6=3(n+2)........................................to(2)#

Here, #(6)+(2)=8 and (6)xx(2)=12#

So ,

#n^2+color(red)(8n)+12=n^2color(red)(+6n+2n)+12#

#n^2+8n+12=n(n+6)+2(n+6)#

#n^2+8n+12=(n+6)(n+2).....................to(3)#

From #(1),(2) and (3)#

#P=(3cancel((n+2)))/((n+6)cancel((n+2)))#

#:.P=3/(n+6)#

Julia Adams · Answer

undefined To simplify the expression (8n-3)/(n^2+8n+12)-(5n-9)/(n^2+8n+12), we can combine the two fractions by finding a common denominator. Since both fractions have the same denominator, we can subtract the numerators directly.

The common denominator is (n^2+8n+12).

Subtracting the numerators, we get (8n-3)-(5n-9) = 8n-3-5n+9 = 3n+6.

Therefore, the simplified expression is (3n+6)/(n^2+8n+12).