Solve (4/28x^3+5/21x^2+3/7x)*7x^3

$$( \frac { 4 } { 28 x ^ { 3 } } + \frac { 5 } { 21 x ^ { 2 } } + \frac { 3 } { 7 x } ) \cdot 7 x ^ { 3 }$$

Evaluate

$$3x^{2}+\frac{5x}{3}+1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 28x^{3} and 21x^{2} is 84x^{3}. Multiply \frac{4}{28x^{3}} times \frac{3}{3}. Multiply \frac{5}{21x^{2}} times \frac{4x}{4x}.

$$\left(\frac{4\times 3}{84x^{3}}+\frac{5\times 4x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Since \frac{4\times 3}{84x^{3}} and \frac{5\times 4x}{84x^{3}} have the same denominator, add them by adding their numerators.

$$\left(\frac{4\times 3+5\times 4x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Do the multiplications in 4\times 3+5\times 4x.

$$\left(\frac{12+20x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Factor the expressions that are not already factored in \frac{12+20x}{84x^{3}}.

$$\left(\frac{4\left(5x+3\right)}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Cancel out 4 in both numerator and denominator.

$$\left(\frac{5x+3}{21x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21x^{3} and 7x is 21x^{3}. Multiply \frac{3}{7x} times \frac{3x^{2}}{3x^{2}}.

$$\left(\frac{5x+3}{21x^{3}}+\frac{3\times 3x^{2}}{21x^{3}}\right)\times 7x^{3}$$

Since \frac{5x+3}{21x^{3}} and \frac{3\times 3x^{2}}{21x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{5x+3+3\times 3x^{2}}{21x^{3}}\times 7x^{3}$$

Do the multiplications in 5x+3+3\times 3x^{2}.

$$\frac{5x+3+9x^{2}}{21x^{3}}\times 7x^{3}$$

Express \frac{5x+3+9x^{2}}{21x^{3}}\times 7 as a single fraction.

$$\frac{\left(5x+3+9x^{2}\right)\times 7}{21x^{3}}x^{3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{9x^{2}+5x+3}{3x^{3}}x^{3}$$

Express \frac{9x^{2}+5x+3}{3x^{3}}x^{3} as a single fraction.

$$\frac{\left(9x^{2}+5x+3\right)x^{3}}{3x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{9x^{2}+5x+3}{3}$$

Expand

$$3x^{2}+\frac{5x}{3}+1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 28x^{3} and 21x^{2} is 84x^{3}. Multiply \frac{4}{28x^{3}} times \frac{3}{3}. Multiply \frac{5}{21x^{2}} times \frac{4x}{4x}.

$$\left(\frac{4\times 3}{84x^{3}}+\frac{5\times 4x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Since \frac{4\times 3}{84x^{3}} and \frac{5\times 4x}{84x^{3}} have the same denominator, add them by adding their numerators.

$$\left(\frac{4\times 3+5\times 4x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Do the multiplications in 4\times 3+5\times 4x.

$$\left(\frac{12+20x}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Factor the expressions that are not already factored in \frac{12+20x}{84x^{3}}.

$$\left(\frac{4\left(5x+3\right)}{84x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

Cancel out 4 in both numerator and denominator.

$$\left(\frac{5x+3}{21x^{3}}+\frac{3}{7x}\right)\times 7x^{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21x^{3} and 7x is 21x^{3}. Multiply \frac{3}{7x} times \frac{3x^{2}}{3x^{2}}.

$$\left(\frac{5x+3}{21x^{3}}+\frac{3\times 3x^{2}}{21x^{3}}\right)\times 7x^{3}$$

Since \frac{5x+3}{21x^{3}} and \frac{3\times 3x^{2}}{21x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{5x+3+3\times 3x^{2}}{21x^{3}}\times 7x^{3}$$

Do the multiplications in 5x+3+3\times 3x^{2}.

$$\frac{5x+3+9x^{2}}{21x^{3}}\times 7x^{3}$$

Express \frac{5x+3+9x^{2}}{21x^{3}}\times 7 as a single fraction.

$$\frac{\left(5x+3+9x^{2}\right)\times 7}{21x^{3}}x^{3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{9x^{2}+5x+3}{3x^{3}}x^{3}$$

Express \frac{9x^{2}+5x+3}{3x^{3}}x^{3} as a single fraction.

$$\frac{\left(9x^{2}+5x+3\right)x^{3}}{3x^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{9x^{2}+5x+3}{3}$$