Solve 16x-8x+1/3x*3(x-2)-x(x-2)/x^2-4x+4

$$\frac { 16 x - 8 x + 1 } { 3 x } \times \frac { 3 ( x - 2 ) - x ( x - 2 ) } { x ^ { 2 } - 4 x + 4 }$$

Evaluate

$$\frac{\left(3-x\right)\left(8x+1\right)}{3x\left(x-2\right)}$$

Short Solution Steps

Combine 16x and -8x to get 8x.

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

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

$$\frac{8x+1}{3x}\times \frac{\left(x-2\right)\left(-x+3\right)}{\left(x-2\right)^{2}}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{8x+1}{3x}\times \frac{-x+3}{x-2}$$

Multiply \frac{8x+1}{3x} times \frac{-x+3}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x+1\right)\left(-x+3\right)}{3x\left(x-2\right)}$$

Use the distributive property to multiply 8x+1 by -x+3 and combine like terms.

$$\frac{-8x^{2}+23x+3}{3x\left(x-2\right)}$$

Use the distributive property to multiply 3x by x-2.

$$\frac{-8x^{2}+23x+3}{3x^{2}-6x}$$

Expand

$$-\frac{8x^{2}-23x-3}{3x\left(x-2\right)}$$

Short Solution Steps

Combine 16x and -8x to get 8x.

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

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

$$\frac{8x+1}{3x}\times \frac{\left(x-2\right)\left(-x+3\right)}{\left(x-2\right)^{2}}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{8x+1}{3x}\times \frac{-x+3}{x-2}$$

Multiply \frac{8x+1}{3x} times \frac{-x+3}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x+1\right)\left(-x+3\right)}{3x\left(x-2\right)}$$

Use the distributive property to multiply 8x+1 by -x+3 and combine like terms.

$$\frac{-8x^{2}+23x+3}{3x\left(x-2\right)}$$

Use the distributive property to multiply 3x by x-2.

$$\frac{-8x^{2}+23x+3}{3x^{2}-6x}$$