Question

simplify (5×25^n+1 -25×5^2n) ÷( 5 ×5^2n+3- (25)^n+1)

Answer 1

The simplified answer is $\frac{1}{6}$

Step-by-step explanation:

$\frac{5\times 25^{n+1}-25\times5^{2n} }{5\times 5^{2n+3}-25^{n+1} }\\\\=\frac{5\times 5^{2(n+1)}-25\times5^{2n} }{5\times 5^{2n+3}-5^{2(n+1)} }\\\\=\frac{5\times 5^{2n+2}-25\times5^{2n} }{5\times 5^{2n+3}-5^{2n+2} }\\\\=\frac{5\times 5^{2n}\times 5^{2} -25\times5^{2n} }{5\times 5^{2n}\times5^{3} -5^{2n}\times5^{2} }$

Taking the common factor from both numerator and denominator

$=\frac{5^{2n}\times 5^{2} (5-1)}{5^{2n}\times5^{2} (5^{2} -1 }$

Cancel out the common term from numerator and denominator.

$=\frac{ (5-1)}{ (5^{2} -1 ) }\\\\=\frac{4}{25-1} \\\\=\frac{4}{24} \\\\=\frac{1}{6}$

Learn More:

Simplify

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Answer 2

Step-by-step explanation:

I hope the attachment will help you.