Solve 3x^2-48/6x^2*left(2xright)^3/x^3+10{x^2+24x}

$$\frac{ 3 { x }^{ 2 } -48 }{ 6 { x }^{ 2 } } \times \frac{ { \left(2x \right) }^{ 3 } }{ { x }^{ 3 } +10 { x }^{ 2 } +24x }$$

Evaluate

$$\frac{4\left(x-4\right)}{x+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-48}{6x^{2}}.

$$\frac{3\left(x-4\right)\left(x+4\right)}{6x^{2}}\times \frac{\left(2x\right)^{3}}{x^{3}+10x^{2}+24x}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{\left(2x\right)^{3}}{x^{3}+10x^{2}+24x}$$

Expand \left(2x\right)^{3}.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{2^{3}x^{3}}{x^{3}+10x^{2}+24x}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{3}}{x^{3}+10x^{2}+24x}$$

Factor the expressions that are not already factored in \frac{8x^{3}}{x^{3}+10x^{2}+24x}.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{3}}{x\left(x+4\right)\left(x+6\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{2}}{\left(x+4\right)\left(x+6\right)}$$

Multiply \frac{\left(x-4\right)\left(x+4\right)}{2x^{2}} times \frac{8x^{2}}{\left(x+4\right)\left(x+6\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x+4\right)\times 8x^{2}}{2x^{2}\left(x+4\right)\left(x+6\right)}$$

Cancel out 2\left(x+4\right)x^{2} in both numerator and denominator.

$$\frac{4\left(x-4\right)}{x+6}$$

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

$$\frac{4x-16}{x+6}$$

Expand

$$\frac{4\left(x-4\right)}{x+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-48}{6x^{2}}.

$$\frac{3\left(x-4\right)\left(x+4\right)}{6x^{2}}\times \frac{\left(2x\right)^{3}}{x^{3}+10x^{2}+24x}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{\left(2x\right)^{3}}{x^{3}+10x^{2}+24x}$$

Expand \left(2x\right)^{3}.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{2^{3}x^{3}}{x^{3}+10x^{2}+24x}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{3}}{x^{3}+10x^{2}+24x}$$

Factor the expressions that are not already factored in \frac{8x^{3}}{x^{3}+10x^{2}+24x}.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{3}}{x\left(x+4\right)\left(x+6\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{2x^{2}}\times \frac{8x^{2}}{\left(x+4\right)\left(x+6\right)}$$

Multiply \frac{\left(x-4\right)\left(x+4\right)}{2x^{2}} times \frac{8x^{2}}{\left(x+4\right)\left(x+6\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x+4\right)\times 8x^{2}}{2x^{2}\left(x+4\right)\left(x+6\right)}$$

Cancel out 2\left(x+4\right)x^{2} in both numerator and denominator.

$$\frac{4\left(x-4\right)}{x+6}$$

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

$$\frac{4x-16}{x+6}$$