Solve x-4/4x^2+3x8x^2/7x^2-28x

$$\frac { x - 4 } { 4 x ^ { 2 } + 3 x } \frac { 8 x ^ { 2 } } { 7 x ^ { 2 } - 28 x }$$

Evaluate

$$\frac{8}{7\left(4x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{2}}{7x^{2}-28x}.

$$\frac{x-4}{4x^{2}+3x}\times \frac{8x^{2}}{7x\left(x-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x-4}{4x^{2}+3x}\times \frac{8x}{7\left(x-4\right)}$$

Multiply \frac{x-4}{4x^{2}+3x} times \frac{8x}{7\left(x-4\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\times 8x}{\left(4x^{2}+3x\right)\times 7\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{8x}{7\left(4x^{2}+3x\right)}$$

Factor the expressions that are not already factored.

$$\frac{8x}{7x\left(4x+3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{8}{7\left(4x+3\right)}$$

Expand the expression.

$$\frac{8}{28x+21}$$

Expand

$$\frac{8}{7\left(4x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{2}}{7x^{2}-28x}.

$$\frac{x-4}{4x^{2}+3x}\times \frac{8x^{2}}{7x\left(x-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x-4}{4x^{2}+3x}\times \frac{8x}{7\left(x-4\right)}$$

Multiply \frac{x-4}{4x^{2}+3x} times \frac{8x}{7\left(x-4\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\times 8x}{\left(4x^{2}+3x\right)\times 7\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{8x}{7\left(4x^{2}+3x\right)}$$

Factor the expressions that are not already factored.

$$\frac{8x}{7x\left(4x+3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{8}{7\left(4x+3\right)}$$

Expand the expression.

$$\frac{8}{28x+21}$$