Solve x^2-4x/x^2-15x+54*x^2-x-72/x^2-15x+54

$$\frac{ { x }^{ 2 } -4x }{ { x }^{ 2 } -15x+54 } \times \frac{ { x }^{ 2 } -x-72 }{ { x }^{ 2 } -15x+54 }$$

Evaluate

$$\frac{x\left(x-4\right)\left(x+8\right)}{\left(x-9\right)\left(x-6\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-72}{x^{2}-15x+54}.

$$\frac{x^{2}-4x}{x^{2}-15x+54}\times \frac{\left(x-9\right)\left(x+8\right)}{\left(x-9\right)\left(x-6\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x^{2}-4x}{x^{2}-15x+54}\times \frac{x+8}{x-6}$$

Multiply \frac{x^{2}-4x}{x^{2}-15x+54} times \frac{x+8}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-4x\right)\left(x+8\right)}{\left(x^{2}-15x+54\right)\left(x-6\right)}$$

Use the distributive property to multiply x^{2}-4x by x+8 and combine like terms.

$$\frac{x^{3}+4x^{2}-32x}{\left(x^{2}-15x+54\right)\left(x-6\right)}$$

Use the distributive property to multiply x^{2}-15x+54 by x-6 and combine like terms.

$$\frac{x^{3}+4x^{2}-32x}{x^{3}-21x^{2}+144x-324}$$

Expand

$$\frac{x^{3}+4x^{2}-32x}{\left(x-9\right)\left(x-6\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-72}{x^{2}-15x+54}.

$$\frac{x^{2}-4x}{x^{2}-15x+54}\times \frac{\left(x-9\right)\left(x+8\right)}{\left(x-9\right)\left(x-6\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x^{2}-4x}{x^{2}-15x+54}\times \frac{x+8}{x-6}$$

Multiply \frac{x^{2}-4x}{x^{2}-15x+54} times \frac{x+8}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-4x\right)\left(x+8\right)}{\left(x^{2}-15x+54\right)\left(x-6\right)}$$

Use the distributive property to multiply x^{2}-4x by x+8 and combine like terms.

$$\frac{x^{3}+4x^{2}-32x}{\left(x^{2}-15x+54\right)\left(x-6\right)}$$

Use the distributive property to multiply x^{2}-15x+54 by x-6 and combine like terms.

$$\frac{x^{3}+4x^{2}-32x}{x^{3}-21x^{2}+144x-324}$$