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

$$\frac { 5 ( 1 - 2 x ) } { ( 2 x - 1 ) ^ { 2 } } * x \frac { ( 2 x + 1 ) ( x - 1 ) } { 3 ( x + 1 ) }$$

Evaluate

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

Short Solution Steps

Use the distributive property to multiply 5 by 1-2x.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{\left(2x+1\right)\left(x-1\right)}{3\left(x+1\right)}$$

Use the distributive property to multiply 2x+1 by x-1 and combine like terms.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{2x^{2}-x-1}{3\left(x+1\right)}$$

Use the distributive property to multiply 3 by x+1.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{2x^{2}-x-1}{3x+3}$$

Express \frac{5-10x}{\left(2x-1\right)^{2}}x as a single fraction.

$$\frac{\left(5-10x\right)x}{\left(2x-1\right)^{2}}\times \frac{2x^{2}-x-1}{3x+3}$$

Multiply \frac{\left(5-10x\right)x}{\left(2x-1\right)^{2}} times \frac{2x^{2}-x-1}{3x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5-10x\right)x\left(2x^{2}-x-1\right)}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply 5-10x by x.

$$\frac{\left(5x-10x^{2}\right)\left(2x^{2}-x-1\right)}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply 5x-10x^{2} by 2x^{2}-x-1 and combine like terms.

$$\frac{20x^{3}+5x^{2}-5x-20x^{4}}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply \left(2x-1\right)^{2} by 3x+3.

$$\frac{20x^{3}+5x^{2}-5x-20x^{4}}{3\left(2x-1\right)^{2}x+3\left(2x-1\right)^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out 2x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-10x^{3}+5x^{2}+5x}{6x^{2}+3x-3}$$

Expand

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

Short Solution Steps

Use the distributive property to multiply 5 by 1-2x.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{\left(2x+1\right)\left(x-1\right)}{3\left(x+1\right)}$$

Use the distributive property to multiply 2x+1 by x-1 and combine like terms.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{2x^{2}-x-1}{3\left(x+1\right)}$$

Use the distributive property to multiply 3 by x+1.

$$\frac{5-10x}{\left(2x-1\right)^{2}}x\times \frac{2x^{2}-x-1}{3x+3}$$

Express \frac{5-10x}{\left(2x-1\right)^{2}}x as a single fraction.

$$\frac{\left(5-10x\right)x}{\left(2x-1\right)^{2}}\times \frac{2x^{2}-x-1}{3x+3}$$

Multiply \frac{\left(5-10x\right)x}{\left(2x-1\right)^{2}} times \frac{2x^{2}-x-1}{3x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5-10x\right)x\left(2x^{2}-x-1\right)}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply 5-10x by x.

$$\frac{\left(5x-10x^{2}\right)\left(2x^{2}-x-1\right)}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply 5x-10x^{2} by 2x^{2}-x-1 and combine like terms.

$$\frac{20x^{3}+5x^{2}-5x-20x^{4}}{\left(2x-1\right)^{2}\left(3x+3\right)}$$

Use the distributive property to multiply \left(2x-1\right)^{2} by 3x+3.

$$\frac{20x^{3}+5x^{2}-5x-20x^{4}}{3\left(2x-1\right)^{2}x+3\left(2x-1\right)^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out 2x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-10x^{3}+5x^{2}+5x}{6x^{2}+3x-3}$$