Solve 8x^2-4x/2x^2+5x-3*x^2-9/4x^2

$$\frac { 8 x ^ { 2 } - 4 x } { 2 x ^ { 2 } + 5 x - 3 } \cdot \frac { x ^ { 2 } - 9 } { 4 x ^ { 2 } }$$

Evaluate

$$\frac{x-3}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{2}-4x}{2x^{2}+5x-3}.

$$\frac{4x\left(2x-1\right)}{\left(2x-1\right)\left(x+3\right)}\times \frac{x^{2}-9}{4x^{2}}$$

Cancel out 2x-1 in both numerator and denominator.

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

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

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

Cancel out 4x in both numerator and denominator.

$$\frac{x^{2}-9}{x\left(x+3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{x}$$

Expand

$$\frac{x-3}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{2}-4x}{2x^{2}+5x-3}.

$$\frac{4x\left(2x-1\right)}{\left(2x-1\right)\left(x+3\right)}\times \frac{x^{2}-9}{4x^{2}}$$

Cancel out 2x-1 in both numerator and denominator.

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

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

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

Cancel out 4x in both numerator and denominator.

$$\frac{x^{2}-9}{x\left(x+3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{x}$$