Solve 3950^3/3315000-33950^2/2000+18109(3950)/10625+992

$$\frac{ { 3950 }^{ 3 } }{ 3315000 } - \frac{ 3 { 3950 }^{ 2 } }{ 2000 } + \frac{ 18109(3950) }{ 10625 } +992$$

Evaluate

$$\frac{193049107}{66300}\approx 2911.751236802$$

Solution Steps

Calculate 3950 to the power of 3 and get 61629875000.

$$\frac{61629875000}{3315000}-\frac{3\times 3950^{2}}{2000}+\frac{18109\times 3950}{10625}+992$$

Reduce the fraction \frac{61629875000}{3315000} to lowest terms by extracting and canceling out 5000.

$$\frac{12325975}{663}-\frac{3\times 3950^{2}}{2000}+\frac{18109\times 3950}{10625}+992$$

Calculate 3950 to the power of 2 and get 15602500.

$$\frac{12325975}{663}-\frac{3\times 15602500}{2000}+\frac{18109\times 3950}{10625}+992$$

Multiply 3 and 15602500 to get 46807500.

$$\frac{12325975}{663}-\frac{46807500}{2000}+\frac{18109\times 3950}{10625}+992$$

Reduce the fraction \frac{46807500}{2000} to lowest terms by extracting and canceling out 500.

$$\frac{12325975}{663}-\frac{93615}{4}+\frac{18109\times 3950}{10625}+992$$

Least common multiple of 663 and 4 is 2652. Convert \frac{12325975}{663} and \frac{93615}{4} to fractions with denominator 2652.

$$\frac{49303900}{2652}-\frac{62066745}{2652}+\frac{18109\times 3950}{10625}+992$$

Since \frac{49303900}{2652} and \frac{62066745}{2652} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49303900-62066745}{2652}+\frac{18109\times 3950}{10625}+992$$

Subtract 62066745 from 49303900 to get -12762845.

$$-\frac{12762845}{2652}+\frac{18109\times 3950}{10625}+992$$

Multiply 18109 and 3950 to get 71530550.

$$-\frac{12762845}{2652}+\frac{71530550}{10625}+992$$

Reduce the fraction \frac{71530550}{10625} to lowest terms by extracting and canceling out 25.

$$-\frac{12762845}{2652}+\frac{2861222}{425}+992$$

Least common multiple of 2652 and 425 is 66300. Convert -\frac{12762845}{2652} and \frac{2861222}{425} to fractions with denominator 66300.

$$-\frac{319071125}{66300}+\frac{446350632}{66300}+992$$

Since -\frac{319071125}{66300} and \frac{446350632}{66300} have the same denominator, add them by adding their numerators.

$$\frac{-319071125+446350632}{66300}+992$$

Add -319071125 and 446350632 to get 127279507.

$$\frac{127279507}{66300}+992$$

Convert 992 to fraction \frac{65769600}{66300}.

$$\frac{127279507}{66300}+\frac{65769600}{66300}$$

Since \frac{127279507}{66300} and \frac{65769600}{66300} have the same denominator, add them by adding their numerators.

$$\frac{127279507+65769600}{66300}$$

Add 127279507 and 65769600 to get 193049107.

$$\frac{193049107}{66300}$$

Factor

$$\frac{1367 \cdot 141221}{2 ^ {2} \cdot 3 \cdot 5 ^ {2} \cdot 13 \cdot 17} = 2911\frac{49807}{66300} = 2911.751236802413$$