Solve 2:(7x^2+3x)-1/3(21x^2-12)

$$2 : ( 7 x ^ { 2 } + 3 x ) - \frac { 1 } { 3 } ( 21 x ^ { 2 } - 12 )$$

Evaluate

$$\frac{2+12x+28x^{2}-21x^{3}-49x^{4}}{x\left(7x+3\right)}$$

Short Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 21x^{2}-12.

$$\frac{2}{7x^{2}+3x}-7x^{2}+4$$

Factor 7x^{2}+3x.

$$\frac{2}{x\left(7x+3\right)}-7x^{2}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -7x^{2}+4 times \frac{x\left(7x+3\right)}{x\left(7x+3\right)}.

$$\frac{2}{x\left(7x+3\right)}+\frac{\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)}$$

Since \frac{2}{x\left(7x+3\right)} and \frac{\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{2+\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)}$$

Do the multiplications in 2+\left(-7x^{2}+4\right)x\left(7x+3\right).

$$\frac{2-49x^{4}-21x^{3}+28x^{2}+12x}{x\left(7x+3\right)}$$

Expand x\left(7x+3\right).

$$\frac{2-49x^{4}-21x^{3}+28x^{2}+12x}{7x^{2}+3x}$$

Expand

$$\frac{2+12x+28x^{2}-21x^{3}-49x^{4}}{7x^{2}+3x}$$

Short Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 21x^{2}-12.

$$\frac{2}{7x^{2}+3x}-7x^{2}+4$$

Factor 7x^{2}+3x.

$$\frac{2}{x\left(7x+3\right)}-7x^{2}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -7x^{2}+4 times \frac{x\left(7x+3\right)}{x\left(7x+3\right)}.

$$\frac{2}{x\left(7x+3\right)}+\frac{\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)}$$

Since \frac{2}{x\left(7x+3\right)} and \frac{\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{2+\left(-7x^{2}+4\right)x\left(7x+3\right)}{x\left(7x+3\right)}$$

Do the multiplications in 2+\left(-7x^{2}+4\right)x\left(7x+3\right).

$$\frac{2-49x^{4}-21x^{3}+28x^{2}+12x}{x\left(7x+3\right)}$$

Expand x\left(7x+3\right).

$$\frac{2-49x^{4}-21x^{3}+28x^{2}+12x}{7x^{2}+3x}$$