Solve 100-x^2/x-5*3/x+10*2x^2-50/x^2-5x-50

$$\frac { 100 - x ^ { 2 } } { x - 5 } \cdot \frac { 3 } { x + 10 } \cdot \frac { 2 x ^ { 2 } - 50 } { x ^ { 2 } - 5 x - 50 }$$

Evaluate

$$-6$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-50}{x^{2}-5x-50}.

$$\frac{100-x^{2}}{x-5}\times \frac{3}{x+10}\times \frac{2\left(x-5\right)\left(x+5\right)}{\left(x-10\right)\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{100-x^{2}}{x-5}\times \frac{3}{x+10}\times \frac{2\left(x-5\right)}{x-10}$$

Multiply \frac{100-x^{2}}{x-5} times \frac{3}{x+10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(100-x^{2}\right)\times 3}{\left(x-5\right)\left(x+10\right)}\times \frac{2\left(x-5\right)}{x-10}$$

Multiply \frac{\left(100-x^{2}\right)\times 3}{\left(x-5\right)\left(x+10\right)} times \frac{2\left(x-5\right)}{x-10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(100-x^{2}\right)\times 3\times 2\left(x-5\right)}{\left(x-5\right)\left(x+10\right)\left(x-10\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{2\times 3\left(-x^{2}+100\right)}{\left(x-10\right)\left(x+10\right)}$$

Multiply 2 and 3 to get 6.

$$\frac{6\left(-x^{2}+100\right)}{\left(x-10\right)\left(x+10\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(x-10\right)\left(-x-10\right)}{\left(x-10\right)\left(x+10\right)}$$

Extract the negative sign in -10-x.

$$\frac{-6\left(x-10\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

Cancel out \left(x-10\right)\left(x+10\right) in both numerator and denominator.

$$-6$$

Factor

$$-6$$