Solve 7x+35/x^3+10x^2+25x*x^2-25/7x+14

$$\frac { 7 x + 35 } { x ^ { 3 } + 10 x ^ { 2 } + 25 x } \cdot \frac { x ^ { 2 } - 25 } { 7 x + 14 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{7x+35}{x^{3}+10x^{2}+25x}.

$$\frac{7\left(x+5\right)}{x\left(x+5\right)^{2}}\times \frac{x^{2}-25}{7x+14}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{7}{x\left(x+5\right)}\times \frac{x^{2}-25}{7x+14}$$

Multiply \frac{7}{x\left(x+5\right)} times \frac{x^{2}-25}{7x+14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(x^{2}-25\right)}{x\left(x+5\right)\left(7x+14\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 7\left(x+5\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{7x+35}{x^{3}+10x^{2}+25x}.

$$\frac{7\left(x+5\right)}{x\left(x+5\right)^{2}}\times \frac{x^{2}-25}{7x+14}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{7}{x\left(x+5\right)}\times \frac{x^{2}-25}{7x+14}$$

Multiply \frac{7}{x\left(x+5\right)} times \frac{x^{2}-25}{7x+14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(x^{2}-25\right)}{x\left(x+5\right)\left(7x+14\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 7\left(x+5\right) in both numerator and denominator.

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

Expand the expression.

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