Solve frac{10x^{2}-20x}{40x^3-80x^2}*16x^3+80x^2/6x+30

$$\frac { 10 x ^ { 2 } - 20 x } { 40 x ^ { 3 } - 80 x ^ { 2 } } \cdot \frac { 16 x ^ { 3 } + 80 x ^ { 2 } } { 6 x + 30 }$$

Evaluate

$$\frac{2x}{3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{10x^{2}-20x}{40x^{3}-80x^{2}}.

$$\frac{10x\left(x-2\right)}{40\left(x-2\right)x^{2}}\times \frac{16x^{3}+80x^{2}}{6x+30}$$

Cancel out 10x\left(x-2\right) in both numerator and denominator.

$$\frac{1}{4x}\times \frac{16x^{3}+80x^{2}}{6x+30}$$

Factor the expressions that are not already factored in \frac{16x^{3}+80x^{2}}{6x+30}.

$$\frac{1}{4x}\times \frac{16\left(x+5\right)x^{2}}{6\left(x+5\right)}$$

Cancel out 2\left(x+5\right) in both numerator and denominator.

$$\frac{1}{4x}\times \frac{8x^{2}}{3}$$

Multiply \frac{1}{4x} times \frac{8x^{2}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8x^{2}}{4x\times 3}$$

Cancel out 4x in both numerator and denominator.

$$\frac{2x}{3}$$

Expand

$$\frac{2x}{3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{10x^{2}-20x}{40x^{3}-80x^{2}}.

$$\frac{10x\left(x-2\right)}{40\left(x-2\right)x^{2}}\times \frac{16x^{3}+80x^{2}}{6x+30}$$

Cancel out 10x\left(x-2\right) in both numerator and denominator.

$$\frac{1}{4x}\times \frac{16x^{3}+80x^{2}}{6x+30}$$

Factor the expressions that are not already factored in \frac{16x^{3}+80x^{2}}{6x+30}.

$$\frac{1}{4x}\times \frac{16\left(x+5\right)x^{2}}{6\left(x+5\right)}$$

Cancel out 2\left(x+5\right) in both numerator and denominator.

$$\frac{1}{4x}\times \frac{8x^{2}}{3}$$

Multiply \frac{1}{4x} times \frac{8x^{2}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8x^{2}}{4x\times 3}$$

Cancel out 4x in both numerator and denominator.

$$\frac{2x}{3}$$