Question

simplify 10×5^n+1 + 25×5^n/3×5^n+2 + 10×5^n+1​

Answer 1

What is (10×5^ (n+1) +25×5^(n) )/(3×5^(n+2) +10×5^(n+1))?

The way the question is written is not right. If the part before division is numerator and rest denominator (Which is most likely), then the answer written by , is right.

You need to eliminate the annoying exponent factor. And it is easy to convert all such factors to 5^(n+1).

Numerator =10.5^(n+1)+5.5.5^(n) =10.5^(n+1)+5.5^(n+1) =15.5^(n+1)

Denominator =3.5.5^(n+1)+10.5^(n+1) = 15.5^(n+1)+10.5^(n+1) =25.5^(n+1)

Now in the given question the factor 5^(n+1) is removed from numerator and denominator, thus it reduces to 15/25 =3/5.