Solve x^2-25/x^2+8x+15*x^2+3x/2x

$$\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 8 x + 15 } \cdot \frac { x ^ { 2 } + 3 x } { 2 x }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-25}{x^{2}+8x+15}.

$$\frac{\left(x-5\right)\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}\times \frac{x^{2}+3x}{2x}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{x+3}\times \frac{x^{2}+3x}{2x}$$

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

$$\frac{x-5}{x+3}\times \frac{x\left(x+3\right)}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{x-5}{x+3}\times \frac{x+3}{2}$$

Multiply \frac{x-5}{x+3} times \frac{x+3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-5\right)\left(x+3\right)}{\left(x+3\right)\times 2}$$

Cancel out x+3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-25}{x^{2}+8x+15}.

$$\frac{\left(x-5\right)\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}\times \frac{x^{2}+3x}{2x}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{x+3}\times \frac{x^{2}+3x}{2x}$$

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

$$\frac{x-5}{x+3}\times \frac{x\left(x+3\right)}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{x-5}{x+3}\times \frac{x+3}{2}$$

Multiply \frac{x-5}{x+3} times \frac{x+3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-5\right)\left(x+3\right)}{\left(x+3\right)\times 2}$$

Cancel out x+3 in both numerator and denominator.

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