Solve [frac{x^{2}-49}{x^{2}+7x}][frac{x^{3}-343}{x^3-2x^2-35x}][x^2-7x/x^2+7x+49]

$$[ \frac { x ^ { 2 } - 49 } { x ^ { 2 } + 7 x } ] [ \frac { x ^ { 3 } - 343 } { x ^ { 3 } - 2 x ^ { 2 } - 35 x } ] [ \frac { x ^ { 2 } - 7 x } { x ^ { 2 } + 7 x + 49 } ]$$

Evaluate

$$\frac{\left(x-7\right)^{2}}{x\left(x+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-49}{x^{2}+7x}.

$$\frac{\left(x-7\right)\left(x+7\right)}{x\left(x+7\right)}\times \frac{x^{3}-343}{x^{3}-2x^{2}-35x}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{x-7}{x}\times \frac{x^{3}-343}{x^{3}-2x^{2}-35x}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Factor the expressions that are not already factored in \frac{x^{3}-343}{x^{3}-2x^{2}-35x}.

$$\frac{x-7}{x}\times \frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{x\left(x-7\right)\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x-7}{x}\times \frac{x^{2}+7x+49}{x\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Multiply \frac{x-7}{x} times \frac{x^{2}+7x+49}{x\left(x+5\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{xx\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Multiply \frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{xx\left(x+5\right)} times \frac{x^{2}-7x}{x^{2}+7x+49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x^{2}+7x+49\right)\left(x^{2}-7x\right)}{xx\left(x+5\right)\left(x^{2}+7x+49\right)}$$

Cancel out x^{2}+7x+49 in both numerator and denominator.

$$\frac{\left(x-7\right)\left(x^{2}-7x\right)}{xx\left(x+5\right)}$$

Multiply x and x to get x^{2}.

$$\frac{\left(x-7\right)\left(x^{2}-7x\right)}{x^{2}\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-7\right)^{2}}{\left(x+5\right)x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(x-7\right)^{2}}{x\left(x+5\right)}$$

Expand the expression.

$$\frac{x^{2}-14x+49}{x^{2}+5x}$$

Expand

$$\frac{x^{2}-14x+49}{x\left(x+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-49}{x^{2}+7x}.

$$\frac{\left(x-7\right)\left(x+7\right)}{x\left(x+7\right)}\times \frac{x^{3}-343}{x^{3}-2x^{2}-35x}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{x-7}{x}\times \frac{x^{3}-343}{x^{3}-2x^{2}-35x}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Factor the expressions that are not already factored in \frac{x^{3}-343}{x^{3}-2x^{2}-35x}.

$$\frac{x-7}{x}\times \frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{x\left(x-7\right)\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x-7}{x}\times \frac{x^{2}+7x+49}{x\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Multiply \frac{x-7}{x} times \frac{x^{2}+7x+49}{x\left(x+5\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{xx\left(x+5\right)}\times \frac{x^{2}-7x}{x^{2}+7x+49}$$

Multiply \frac{\left(x-7\right)\left(x^{2}+7x+49\right)}{xx\left(x+5\right)} times \frac{x^{2}-7x}{x^{2}+7x+49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x^{2}+7x+49\right)\left(x^{2}-7x\right)}{xx\left(x+5\right)\left(x^{2}+7x+49\right)}$$

Cancel out x^{2}+7x+49 in both numerator and denominator.

$$\frac{\left(x-7\right)\left(x^{2}-7x\right)}{xx\left(x+5\right)}$$

Multiply x and x to get x^{2}.

$$\frac{\left(x-7\right)\left(x^{2}-7x\right)}{x^{2}\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-7\right)^{2}}{\left(x+5\right)x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(x-7\right)^{2}}{x\left(x+5\right)}$$

Expand the expression.

$$\frac{x^{2}-14x+49}{x^{2}+5x}$$