Solve =1/frac{(1.04)^2-1{0.04}}+0.04

$$= \frac { 1 } { \frac { ( 1.04 ) ^ { 2 } - 1 } { 0.04 } } + 0.04$$

Evaluate

$$\frac{676}{1275}\approx 0.530196078$$

Solution Steps

Divide 1 by \frac{1.04^{2}-1}{0.04} by multiplying 1 by the reciprocal of \frac{1.04^{2}-1}{0.04}.

$$\frac{0.04}{1.04^{2}-1}+0.04$$

Calculate 1.04 to the power of 2 and get 1.0816.

$$\frac{0.04}{1.0816-1}+0.04$$

Subtract 1 from 1.0816 to get 0.0816.

$$\frac{0.04}{0.0816}+0.04$$

Expand \frac{0.04}{0.0816} by multiplying both numerator and the denominator by 10000.

$$\frac{400}{816}+0.04$$

Reduce the fraction \frac{400}{816} to lowest terms by extracting and canceling out 16.

$$\frac{25}{51}+0.04$$

Convert decimal number 0.04 to fraction \frac{4}{100}. Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{25}{51}+\frac{1}{25}$$

Least common multiple of 51 and 25 is 1275. Convert \frac{25}{51} and \frac{1}{25} to fractions with denominator 1275.

$$\frac{625}{1275}+\frac{51}{1275}$$

Since \frac{625}{1275} and \frac{51}{1275} have the same denominator, add them by adding their numerators.

$$\frac{625+51}{1275}$$

Add 625 and 51 to get 676.

$$\frac{676}{1275}$$

Factor

$$\frac{2 ^ {2} \cdot 13 ^ {2}}{3 \cdot 17 \cdot 5 ^ {2}} = 0.5301960784313725$$