Solve 4x^2-9/6x+9*2x/x^2-3

$$\frac { 4 x ^ { 2 } - 9 } { 6 x + 9 } \times \frac { 2 x } { x ^ { 2 } - 3 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{4x^{2}-9}{6x+9}.

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

Cancel out 2x+3 in both numerator and denominator.

$$\frac{2x-3}{3}\times \frac{2x}{x^{2}-3}$$

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

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

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

$$\frac{\left(4x-6\right)x}{3\left(x^{2}-3\right)}$$

Use the distributive property to multiply 4x-6 by x.

$$\frac{4x^{2}-6x}{3\left(x^{2}-3\right)}$$

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

$$\frac{4x^{2}-6x}{3x^{2}-9}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{4x^{2}-9}{6x+9}.

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

Cancel out 2x+3 in both numerator and denominator.

$$\frac{2x-3}{3}\times \frac{2x}{x^{2}-3}$$

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

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

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

$$\frac{\left(4x-6\right)x}{3\left(x^{2}-3\right)}$$

Use the distributive property to multiply 4x-6 by x.

$$\frac{4x^{2}-6x}{3\left(x^{2}-3\right)}$$

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

$$\frac{4x^{2}-6x}{3x^{2}-9}$$