Solve (x-10)(x+3/x^2-7x-30+x+4/x^2-6x-40)

$$(x-10)( \frac{ x+3 }{ { x }^{ 2 } -7x-30 } + \frac{ x+4 }{ { x }^{ 2 } -6x-40 } )$$

Evaluate

$$2$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x+3}{x^{2}-7x-30}.

$$\left(x-10\right)\left(\frac{x+3}{\left(x-10\right)\left(x+3\right)}+\frac{x+4}{x^{2}-6x-40}\right)$$

Cancel out x+3 in both numerator and denominator.

$$\left(x-10\right)\left(\frac{1}{x-10}+\frac{x+4}{x^{2}-6x-40}\right)$$

Factor the expressions that are not already factored in \frac{x+4}{x^{2}-6x-40}.

$$\left(x-10\right)\left(\frac{1}{x-10}+\frac{x+4}{\left(x-10\right)\left(x+4\right)}\right)$$

Cancel out x+4 in both numerator and denominator.

$$\left(x-10\right)\left(\frac{1}{x-10}+\frac{1}{x-10}\right)$$

Combine \frac{1}{x-10} and \frac{1}{x-10} to get 2\times \frac{1}{x-10}.

$$\left(x-10\right)\times 2\times \frac{1}{x-10}$$

Express 2\times \frac{1}{x-10} as a single fraction.

$$\left(x-10\right)\times \frac{2}{x-10}$$

Cancel out x-10 and x-10.

$$2$$

Factor

$$2$$