Solve frac{4x^{2}}{3x^{2}-2x}*15x^2-10x/4x^3-3x^2*16x^2-9/12x

$$\frac { 4 x ^ { 2 } } { 3 x ^ { 2 } - 2 x } \times \frac { 15 x ^ { 2 } - 10 x } { 4 x ^ { 3 } - 3 x ^ { 2 } } \times \frac { 16 x ^ { 2 } - 9 } { 12 x }$$

Evaluate

$$\frac{20}{3}+\frac{5}{x}$$

Short Solution Steps

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

$$\frac{4x^{2}}{x\left(3x-2\right)}\times \frac{15x^{2}-10x}{4x^{3}-3x^{2}}\times \frac{16x^{2}-9}{12x}$$

Cancel out x in both numerator and denominator.

$$\frac{4x}{3x-2}\times \frac{15x^{2}-10x}{4x^{3}-3x^{2}}\times \frac{16x^{2}-9}{12x}$$

Factor the expressions that are not already factored in \frac{15x^{2}-10x}{4x^{3}-3x^{2}}.

$$\frac{4x}{3x-2}\times \frac{5x\left(3x-2\right)}{\left(4x-3\right)x^{2}}\times \frac{16x^{2}-9}{12x}$$

Cancel out x in both numerator and denominator.

$$\frac{4x}{3x-2}\times \frac{5\left(3x-2\right)}{x\left(4x-3\right)}\times \frac{16x^{2}-9}{12x}$$

Multiply \frac{4x}{3x-2} times \frac{5\left(3x-2\right)}{x\left(4x-3\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x\times 5\left(3x-2\right)}{\left(3x-2\right)x\left(4x-3\right)}\times \frac{16x^{2}-9}{12x}$$

Cancel out x\left(3x-2\right) in both numerator and denominator.

$$\frac{4\times 5}{4x-3}\times \frac{16x^{2}-9}{12x}$$

Multiply \frac{4\times 5}{4x-3} times \frac{16x^{2}-9}{12x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5\left(16x^{2}-9\right)}{\left(4x-3\right)\times 12x}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5\left(16x^{2}-9\right)}{3x\left(4x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4x-3 in both numerator and denominator.

$$\frac{5\left(4x+3\right)}{3x}$$

Expand the expression.

$$\frac{20x+15}{3x}$$

Expand

$$\frac{20}{3}+\frac{5}{x}$$

Short Solution Steps

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

$$\frac{4x^{2}}{x\left(3x-2\right)}\times \frac{15x^{2}-10x}{4x^{3}-3x^{2}}\times \frac{16x^{2}-9}{12x}$$

Cancel out x in both numerator and denominator.

$$\frac{4x}{3x-2}\times \frac{15x^{2}-10x}{4x^{3}-3x^{2}}\times \frac{16x^{2}-9}{12x}$$

Factor the expressions that are not already factored in \frac{15x^{2}-10x}{4x^{3}-3x^{2}}.

$$\frac{4x}{3x-2}\times \frac{5x\left(3x-2\right)}{\left(4x-3\right)x^{2}}\times \frac{16x^{2}-9}{12x}$$

Cancel out x in both numerator and denominator.

$$\frac{4x}{3x-2}\times \frac{5\left(3x-2\right)}{x\left(4x-3\right)}\times \frac{16x^{2}-9}{12x}$$

Multiply \frac{4x}{3x-2} times \frac{5\left(3x-2\right)}{x\left(4x-3\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x\times 5\left(3x-2\right)}{\left(3x-2\right)x\left(4x-3\right)}\times \frac{16x^{2}-9}{12x}$$

Cancel out x\left(3x-2\right) in both numerator and denominator.

$$\frac{4\times 5}{4x-3}\times \frac{16x^{2}-9}{12x}$$

Multiply \frac{4\times 5}{4x-3} times \frac{16x^{2}-9}{12x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5\left(16x^{2}-9\right)}{\left(4x-3\right)\times 12x}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5\left(16x^{2}-9\right)}{3x\left(4x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4x-3 in both numerator and denominator.

$$\frac{5\left(4x+3\right)}{3x}$$

Expand the expression.

$$\frac{20x+15}{3x}$$