Solve frac{(-2x^{2}-6x^{-3})+2x(x)+2/x+3/2x^{2}}{2x^4-6x^-1+2x^2+2x+2/x+3/x^2}

$$\frac { ( - 2 x ^ { 2 } - 6 x ^ { - 3 } ) + 2 x ( x ) + \frac { 2 } { x } + \frac { 3 } { 2 x ^ { 2 } } } { 2 x ^ { 4 } - 6 x ^ { - 1 } + 2 x ^ { 2 } + 2 x + \frac { 2 } { x } + \frac { 3 } { x ^ { 2 } } }$$

Evaluate

$$\frac{4x^{2}+3x-12}{2x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Short Solution Steps

Multiply x and x to get x^{2}.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -6x^{-3} times \frac{x}{x}.

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

Since \frac{-6x^{-3}x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -6x^{-3}x+2.

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

Factor the expressions that are not already factored in \frac{-6x^{-2}+2}{x}.

$$\frac{\frac{2x^{-2}\left(x^{2}-3\right)}{x}+\frac{3}{2x^{2}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{2\left(x^{2}-3\right)}{x^{3}}+\frac{3}{2x^{2}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\times 2\left(x^{2}-3\right)}{2x^{3}}+\frac{3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\times 2\left(x^{2}-3\right)+3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{4x^{2}-12+3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

Factor the expressions that are not already factored in \frac{4x^{2}-12+3x}{2x^{3}}.

$$\frac{\frac{4\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{4}-6x^{-1}+2x^{2}+2x times \frac{x}{x}.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x}{x}+\frac{2}{x}+\frac{3}{x^{2}}}$$

Since \frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x+2}{x}+\frac{3}{x^{2}}}$$

Do the multiplications in \left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x+2.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{5}-6+2x^{3}+2x^{2}+2}{x}+\frac{3}{x^{2}}}$$

Combine like terms in 2x^{5}-6+2x^{3}+2x^{2}+2.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{5}-4+2x^{3}+2x^{2}}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x}{x^{2}}+\frac{3}{x^{2}}}$$

Since \frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x}{x^{2}} and \frac{3}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x+3}{x^{2}}}$$

Do the multiplications in \left(2x^{5}-4+2x^{3}+2x^{2}\right)x+3.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}}}$$

Divide \frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}} by \frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}} by multiplying \frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}} by the reciprocal of \frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}}.

$$\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)x^{2}}{x^{3}\left(2x^{6}-4x+2x^{4}+2x^{3}+3\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

To find the opposite of -\frac{1}{8}\sqrt{201}-\frac{3}{8}, find the opposite of each term.

$$\frac{2\left(x+\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

To find the opposite of \frac{1}{8}\sqrt{201}-\frac{3}{8}, find the opposite of each term.

$$\frac{2\left(x+\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)\left(x-\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply 2 by x+\frac{1}{8}\sqrt{201}+\frac{3}{8}.

$$\frac{\left(2x+\frac{1}{4}\sqrt{201}+\frac{3}{4}\right)\left(x-\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply 2x+\frac{1}{4}\sqrt{201}+\frac{3}{4} by x-\frac{1}{8}\sqrt{201}+\frac{3}{8} and combine like terms.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{1}{32}\left(\sqrt{201}\right)^{2}+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

The square of \sqrt{201} is 201.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{1}{32}\times 201+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Multiply -\frac{1}{32} and 201 to get -\frac{201}{32}.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{201}{32}+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Add -\frac{201}{32} and \frac{9}{32} to get -6.

$$\frac{2x^{2}+\frac{3}{2}x-6}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply x by 2x^{6}+2x^{4}+2x^{3}-4x+3.

$$\frac{2x^{2}+\frac{3}{2}x-6}{2x^{7}+2x^{5}+2x^{4}-4x^{2}+3x}$$

Expand

$$\frac{4x^{2}+3x-12}{2x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Short Solution Steps

Multiply x and x to get x^{2}.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -6x^{-3} times \frac{x}{x}.

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

Since \frac{-6x^{-3}x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -6x^{-3}x+2.

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

Factor the expressions that are not already factored in \frac{-6x^{-2}+2}{x}.

$$\frac{\frac{2x^{-2}\left(x^{2}-3\right)}{x}+\frac{3}{2x^{2}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{2\left(x^{2}-3\right)}{x^{3}}+\frac{3}{2x^{2}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\times 2\left(x^{2}-3\right)}{2x^{3}}+\frac{3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\times 2\left(x^{2}-3\right)+3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{4x^{2}-12+3x}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

Factor the expressions that are not already factored in \frac{4x^{2}-12+3x}{2x^{3}}.

$$\frac{\frac{4\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{2x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{2x^{4}-6x^{-1}+2x^{2}+2x+\frac{2}{x}+\frac{3}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{4}-6x^{-1}+2x^{2}+2x times \frac{x}{x}.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x}{x}+\frac{2}{x}+\frac{3}{x^{2}}}$$

Since \frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x+2}{x}+\frac{3}{x^{2}}}$$

Do the multiplications in \left(2x^{4}-6x^{-1}+2x^{2}+2x\right)x+2.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{5}-6+2x^{3}+2x^{2}+2}{x}+\frac{3}{x^{2}}}$$

Combine like terms in 2x^{5}-6+2x^{3}+2x^{2}+2.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{5}-4+2x^{3}+2x^{2}}{x}+\frac{3}{x^{2}}}$$

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

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x}{x^{2}}+\frac{3}{x^{2}}}$$

Since \frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x}{x^{2}} and \frac{3}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{\left(2x^{5}-4+2x^{3}+2x^{2}\right)x+3}{x^{2}}}$$

Do the multiplications in \left(2x^{5}-4+2x^{3}+2x^{2}\right)x+3.

$$\frac{\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}}}{\frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}}}$$

Divide \frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}} by \frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}} by multiplying \frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x^{3}} by the reciprocal of \frac{2x^{6}-4x+2x^{4}+2x^{3}+3}{x^{2}}.

$$\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)x^{2}}{x^{3}\left(2x^{6}-4x+2x^{4}+2x^{3}+3\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{2\left(x-\left(-\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

To find the opposite of -\frac{1}{8}\sqrt{201}-\frac{3}{8}, find the opposite of each term.

$$\frac{2\left(x+\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)\left(x-\left(\frac{1}{8}\sqrt{201}-\frac{3}{8}\right)\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

To find the opposite of \frac{1}{8}\sqrt{201}-\frac{3}{8}, find the opposite of each term.

$$\frac{2\left(x+\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)\left(x-\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply 2 by x+\frac{1}{8}\sqrt{201}+\frac{3}{8}.

$$\frac{\left(2x+\frac{1}{4}\sqrt{201}+\frac{3}{4}\right)\left(x-\frac{1}{8}\sqrt{201}+\frac{3}{8}\right)}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply 2x+\frac{1}{4}\sqrt{201}+\frac{3}{4} by x-\frac{1}{8}\sqrt{201}+\frac{3}{8} and combine like terms.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{1}{32}\left(\sqrt{201}\right)^{2}+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

The square of \sqrt{201} is 201.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{1}{32}\times 201+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Multiply -\frac{1}{32} and 201 to get -\frac{201}{32}.

$$\frac{2x^{2}+\frac{3}{2}x-\frac{201}{32}+\frac{9}{32}}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Add -\frac{201}{32} and \frac{9}{32} to get -6.

$$\frac{2x^{2}+\frac{3}{2}x-6}{x\left(2x^{6}+2x^{4}+2x^{3}-4x+3\right)}$$

Use the distributive property to multiply x by 2x^{6}+2x^{4}+2x^{3}-4x+3.

$$\frac{2x^{2}+\frac{3}{2}x-6}{2x^{7}+2x^{5}+2x^{4}-4x^{2}+3x}$$