Solve (122x/14+x^21356x/1841x)*x^2/3567

$$( \frac{ 122x }{ 14 } + { x }^{ 2 } \frac { 1356x } { 1841x } ) \times \frac{ { x }^{ 2 } }{ 3567 }$$

Evaluate

$$\frac{\left(1356x+16043\right)x^{3}}{6566847}$$

Short Solution Steps

Divide 122x by 14 to get \frac{61}{7}x.

$$\left(\frac{61}{7}x+x^{2}\times \frac{1356x}{1841x}\right)\times \frac{x^{2}}{3567}$$

Cancel out x in both numerator and denominator.

$$\left(\frac{61}{7}x+x^{2}\times \frac{1356}{1841}\right)\times \frac{x^{2}}{3567}$$

Use the distributive property to multiply \frac{61}{7}x+x^{2}\times \frac{1356}{1841} by \frac{x^{2}}{3567}.

$$\frac{61}{7}x\times \frac{x^{2}}{3567}+\frac{1356}{1841}x^{2}\times \frac{x^{2}}{3567}$$

Multiply \frac{61}{7} times \frac{x^{2}}{3567} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{1356}{1841}x^{2}\times \frac{x^{2}}{3567}$$

Multiply \frac{1356}{1841} times \frac{x^{2}}{3567} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{1356x^{2}}{1841\times 3567}x^{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Multiply 7 and 3567 to get 24969.

$$\frac{61x^{2}}{24969}x+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Express \frac{61x^{2}}{24969}x as a single fraction.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Multiply 1189 and 1841 to get 2188949.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}}{2188949}x^{2}$$

Express \frac{452x^{2}}{2188949}x^{2} as a single fraction.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}x^{2}}{2188949}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24969 and 2188949 is 6566847. Multiply \frac{61x^{2}x}{24969} times \frac{263}{263}. Multiply \frac{452x^{2}x^{2}}{2188949} times \frac{3}{3}.

$$\frac{263\times 61x^{2}x}{6566847}+\frac{3\times 452x^{2}x^{2}}{6566847}$$

Since \frac{263\times 61x^{2}x}{6566847} and \frac{3\times 452x^{2}x^{2}}{6566847} have the same denominator, add them by adding their numerators.

$$\frac{263\times 61x^{2}x+3\times 452x^{2}x^{2}}{6566847}$$

Do the multiplications in 263\times 61x^{2}x+3\times 452x^{2}x^{2}.

$$\frac{16043x^{3}+1356x^{4}}{6566847}$$

Expand

$$\frac{452x^{4}}{2188949}+\frac{61x^{3}}{24969}$$

Short Solution Steps

Divide 122x by 14 to get \frac{61}{7}x.

$$\left(\frac{61}{7}x+x^{2}\times \frac{1356x}{1841x}\right)\times \frac{x^{2}}{3567}$$

Cancel out x in both numerator and denominator.

$$\left(\frac{61}{7}x+x^{2}\times \frac{1356}{1841}\right)\times \frac{x^{2}}{3567}$$

Use the distributive property to multiply \frac{61}{7}x+x^{2}\times \frac{1356}{1841} by \frac{x^{2}}{3567}.

$$\frac{61}{7}x\times \frac{x^{2}}{3567}+\frac{1356}{1841}x^{2}\times \frac{x^{2}}{3567}$$

Multiply \frac{61}{7} times \frac{x^{2}}{3567} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{1356}{1841}x^{2}\times \frac{x^{2}}{3567}$$

Multiply \frac{1356}{1841} times \frac{x^{2}}{3567} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{1356x^{2}}{1841\times 3567}x^{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{61x^{2}}{7\times 3567}x+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Multiply 7 and 3567 to get 24969.

$$\frac{61x^{2}}{24969}x+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Express \frac{61x^{2}}{24969}x as a single fraction.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}}{1189\times 1841}x^{2}$$

Multiply 1189 and 1841 to get 2188949.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}}{2188949}x^{2}$$

Express \frac{452x^{2}}{2188949}x^{2} as a single fraction.

$$\frac{61x^{2}x}{24969}+\frac{452x^{2}x^{2}}{2188949}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24969 and 2188949 is 6566847. Multiply \frac{61x^{2}x}{24969} times \frac{263}{263}. Multiply \frac{452x^{2}x^{2}}{2188949} times \frac{3}{3}.

$$\frac{263\times 61x^{2}x}{6566847}+\frac{3\times 452x^{2}x^{2}}{6566847}$$

Since \frac{263\times 61x^{2}x}{6566847} and \frac{3\times 452x^{2}x^{2}}{6566847} have the same denominator, add them by adding their numerators.

$$\frac{263\times 61x^{2}x+3\times 452x^{2}x^{2}}{6566847}$$

Do the multiplications in 263\times 61x^{2}x+3\times 452x^{2}x^{2}.

$$\frac{16043x^{3}+1356x^{4}}{6566847}$$