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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Multiply 5 and 2 to get 10.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{5x}{-3x^{4}+12x^{3}-18x^{2}+12x-3}$$

Expand

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

Short Solution Steps

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

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

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

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

Multiply 5 and 2 to get 10.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{5x}{-3x^{4}+12x^{3}-18x^{2}+12x-3}$$