Solve 3x^2-2x+1+x^5/3x^2-2x+1*3x^2-2x

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

Evaluate

$$\frac{x\left(3x^{6}+9x^{3}-12x^{2}+7x-2\right)}{3x^{2}-2x+1}$$

Short Solution Steps

Express \frac{3x^{2}-2x+1+x^{5}}{3x^{2}-2x+1}\times 3 as a single fraction.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3}{3x^{2}-2x+1}x^{2}-2x$$

Express \frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3}{3x^{2}-2x+1}x^{2} as a single fraction.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1}-2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x times \frac{3x^{2}-2x+1}{3x^{2}-2x+1}.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1}+\frac{-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1}$$

Since \frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1} and \frac{-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1}$$

Do the multiplications in \left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}-2x\left(3x^{2}-2x+1\right).

$$\frac{9x^{4}-6x^{3}+3x^{2}+3x^{7}-6x^{3}+4x^{2}-2x}{3x^{2}-2x+1}$$

Combine like terms in 9x^{4}-6x^{3}+3x^{2}+3x^{7}-6x^{3}+4x^{2}-2x.

$$\frac{9x^{4}-12x^{3}+7x^{2}+3x^{7}-2x}{3x^{2}-2x+1}$$

Expand

$$\frac{3x^{7}+9x^{4}-12x^{3}+7x^{2}-2x}{3x^{2}-2x+1}$$

Short Solution Steps

Express \frac{3x^{2}-2x+1+x^{5}}{3x^{2}-2x+1}\times 3 as a single fraction.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3}{3x^{2}-2x+1}x^{2}-2x$$

Express \frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3}{3x^{2}-2x+1}x^{2} as a single fraction.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1}-2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x times \frac{3x^{2}-2x+1}{3x^{2}-2x+1}.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1}+\frac{-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1}$$

Since \frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}}{3x^{2}-2x+1} and \frac{-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}-2x\left(3x^{2}-2x+1\right)}{3x^{2}-2x+1}$$

Do the multiplications in \left(3x^{2}-2x+1+x^{5}\right)\times 3x^{2}-2x\left(3x^{2}-2x+1\right).

$$\frac{9x^{4}-6x^{3}+3x^{2}+3x^{7}-6x^{3}+4x^{2}-2x}{3x^{2}-2x+1}$$

Combine like terms in 9x^{4}-6x^{3}+3x^{2}+3x^{7}-6x^{3}+4x^{2}-2x.

$$\frac{9x^{4}-12x^{3}+7x^{2}+3x^{7}-2x}{3x^{2}-2x+1}$$