Solve 2x^2+3x+1/2x-3-x^2-6x+7/

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

Evaluate

$$\frac{22-29x+17x^{2}-2x^{3}}{2x-3}$$

Short Solution Steps

Anything divided by one gives itself.

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

To find the opposite of x^{2}-6x+7, find the opposite of each term.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -x^{2}+6x-7 times \frac{2x-3}{2x-3}.

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

Since \frac{2x^{2}+3x+1}{2x-3} and \frac{\left(-x^{2}+6x-7\right)\left(2x-3\right)}{2x-3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2x^{2}+3x+1+\left(-x^{2}+6x-7\right)\left(2x-3\right).

$$\frac{2x^{2}+3x+1-2x^{3}+3x^{2}+12x^{2}-18x-14x+21}{2x-3}$$

Combine like terms in 2x^{2}+3x+1-2x^{3}+3x^{2}+12x^{2}-18x-14x+21.

$$\frac{17x^{2}-29x+22-2x^{3}}{2x-3}$$

Expand

$$\frac{22-29x+17x^{2}-2x^{3}}{2x-3}$$

Short Solution Steps

Anything divided by one gives itself.

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

To find the opposite of x^{2}-6x+7, find the opposite of each term.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -x^{2}+6x-7 times \frac{2x-3}{2x-3}.

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

Since \frac{2x^{2}+3x+1}{2x-3} and \frac{\left(-x^{2}+6x-7\right)\left(2x-3\right)}{2x-3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2x^{2}+3x+1+\left(-x^{2}+6x-7\right)\left(2x-3\right).

$$\frac{2x^{2}+3x+1-2x^{3}+3x^{2}+12x^{2}-18x-14x+21}{2x-3}$$

Combine like terms in 2x^{2}+3x+1-2x^{3}+3x^{2}+12x^{2}-18x-14x+21.

$$\frac{17x^{2}-29x+22-2x^{3}}{2x-3}$$