Question

simplify 81*3n+1-9*3n/81*3n+2-3*3n+2

Answer 1

hii...

solution:-- 81*3^n+1-9*3^n/81*3^n+2-3*3^n+2

= 3^n+5-(3^n+2)/3^4*3^n+2-3^n+3

= 3^5*3^n- 1/3^4-3^3*3^n

= 243*3^n- 1/81 - 27*3^n

= 216*3^n - 1/81

= (216*3^n+4 - 1)/ 81

Answer 2

The simplified expression for the given expression is $\frac{72n+27}{78n+53}$

Therefore $\frac{81\times (3n+1)-9\times 3n}{81\times (3n+2)-3\times (3n+2)}=\frac{72n+27}{78n+53}$

Step-by-step explanation:

Given that the expression is $\frac{81\times (3n+1)-9\times 3n}{81\times (3n+2)-3\times (3n+2)}$

To simplify the given expression :

$\frac{81\times (3n+1)-9\times 3n}{81\times (3n+2)-3\times (3n+2)}$

• $=\frac{81(3n)+81(1)-9(3n)}{81(3n)+81(2)-3(3n)-3(2)}$ ( by using the distributive property a(x+y)=ax+ay )

• $=\frac{243n+81-27n}{243n+162-9n-6}$
• $=\frac{216n+81}{234n+156}$
• $=\frac{3(72n+27)}{3(78n+53)}$
• $=\frac{72n+27}{78n+53}$
• Therefore the simplified expression for the given expression is $\frac{72n+27}{78n+53}$

Therefore $\frac{81\times (3n+1)-9\times 3n}{81\times (3n+2)-3\times (3n+2)}=\frac{72n+27}{78n+53}$