Solve x^2-left(x+2right)left(x-2right)50-x/2x-1

$${ x }^{ 2 } - \left( x+2 \right) \left( x-2 \right) \frac{ 50-x }{ 2x-1 }$$

Evaluate

$$\frac{3x^{3}-51x^{2}-4x+200}{2x-1}$$

Short Solution Steps

Express \left(x+2\right)\times \frac{50-x}{2x-1} as a single fraction.

$$x^{2}-\frac{\left(x+2\right)\left(50-x\right)}{2x-1}\left(x-2\right)$$

Use the distributive property to multiply \frac{\left(x+2\right)\left(50-x\right)}{2x-1} by x-2.

$$x^{2}-\left(\frac{\left(x+2\right)\left(50-x\right)}{2x-1}x-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Use the distributive property to multiply x+2 by 50-x and combine like terms.

$$x^{2}-\left(\frac{48x-x^{2}+100}{2x-1}x-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Express \frac{48x-x^{2}+100}{2x-1}x as a single fraction.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Use the distributive property to multiply x+2 by 50-x and combine like terms.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}-2\times \frac{48x-x^{2}+100}{2x-1}\right)$$

Express -2\times \frac{48x-x^{2}+100}{2x-1} as a single fraction.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}+\frac{-2\left(48x-x^{2}+100\right)}{2x-1}\right)$$

Since \frac{\left(48x-x^{2}+100\right)x}{2x-1} and \frac{-2\left(48x-x^{2}+100\right)}{2x-1} have the same denominator, add them by adding their numerators.

$$x^{2}-\frac{\left(48x-x^{2}+100\right)x-2\left(48x-x^{2}+100\right)}{2x-1}$$

Do the multiplications in \left(48x-x^{2}+100\right)x-2\left(48x-x^{2}+100\right).

$$x^{2}-\frac{48x^{2}-x^{3}+100x-96x+2x^{2}-200}{2x-1}$$

Combine like terms in 48x^{2}-x^{3}+100x-96x+2x^{2}-200.

$$x^{2}-\frac{50x^{2}-x^{3}+4x-200}{2x-1}$$

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

$$\frac{x^{2}\left(2x-1\right)}{2x-1}-\frac{50x^{2}-x^{3}+4x-200}{2x-1}$$

Since \frac{x^{2}\left(2x-1\right)}{2x-1} and \frac{50x^{2}-x^{3}+4x-200}{2x-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}\left(2x-1\right)-\left(50x^{2}-x^{3}+4x-200\right)}{2x-1}$$

Do the multiplications in x^{2}\left(2x-1\right)-\left(50x^{2}-x^{3}+4x-200\right).

$$\frac{2x^{3}-x^{2}-50x^{2}+x^{3}-4x+200}{2x-1}$$

Combine like terms in 2x^{3}-x^{2}-50x^{2}+x^{3}-4x+200.

$$\frac{3x^{3}-51x^{2}-4x+200}{2x-1}$$

Expand

$$\frac{3x^{3}-51x^{2}-4x+200}{2x-1}$$

Short Solution Steps

Express \left(x+2\right)\times \frac{50-x}{2x-1} as a single fraction.

$$x^{2}-\frac{\left(x+2\right)\left(50-x\right)}{2x-1}\left(x-2\right)$$

Use the distributive property to multiply \frac{\left(x+2\right)\left(50-x\right)}{2x-1} by x-2.

$$x^{2}-\left(\frac{\left(x+2\right)\left(50-x\right)}{2x-1}x-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Use the distributive property to multiply x+2 by 50-x and combine like terms.

$$x^{2}-\left(\frac{48x-x^{2}+100}{2x-1}x-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Express \frac{48x-x^{2}+100}{2x-1}x as a single fraction.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}-2\times \frac{\left(x+2\right)\left(50-x\right)}{2x-1}\right)$$

Use the distributive property to multiply x+2 by 50-x and combine like terms.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}-2\times \frac{48x-x^{2}+100}{2x-1}\right)$$

Express -2\times \frac{48x-x^{2}+100}{2x-1} as a single fraction.

$$x^{2}-\left(\frac{\left(48x-x^{2}+100\right)x}{2x-1}+\frac{-2\left(48x-x^{2}+100\right)}{2x-1}\right)$$

Since \frac{\left(48x-x^{2}+100\right)x}{2x-1} and \frac{-2\left(48x-x^{2}+100\right)}{2x-1} have the same denominator, add them by adding their numerators.

$$x^{2}-\frac{\left(48x-x^{2}+100\right)x-2\left(48x-x^{2}+100\right)}{2x-1}$$

Do the multiplications in \left(48x-x^{2}+100\right)x-2\left(48x-x^{2}+100\right).

$$x^{2}-\frac{48x^{2}-x^{3}+100x-96x+2x^{2}-200}{2x-1}$$

Combine like terms in 48x^{2}-x^{3}+100x-96x+2x^{2}-200.

$$x^{2}-\frac{50x^{2}-x^{3}+4x-200}{2x-1}$$

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

$$\frac{x^{2}\left(2x-1\right)}{2x-1}-\frac{50x^{2}-x^{3}+4x-200}{2x-1}$$

Since \frac{x^{2}\left(2x-1\right)}{2x-1} and \frac{50x^{2}-x^{3}+4x-200}{2x-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}\left(2x-1\right)-\left(50x^{2}-x^{3}+4x-200\right)}{2x-1}$$

Do the multiplications in x^{2}\left(2x-1\right)-\left(50x^{2}-x^{3}+4x-200\right).

$$\frac{2x^{3}-x^{2}-50x^{2}+x^{3}-4x+200}{2x-1}$$

Combine like terms in 2x^{3}-x^{2}-50x^{2}+x^{3}-4x+200.

$$\frac{3x^{3}-51x^{2}-4x+200}{2x-1}$$