Solve x(-20-4)/x+10+-20-x(-20-x)/x+40

$$\frac { x ( - 20 - 4 ) } { x + 10 } + - 20 - \frac { x ( - 20 - x ) } { x + 40 }$$

Evaluate

$$\frac{x^{3}-14x^{2}-1760x-8000}{\left(x+10\right)\left(x+40\right)}$$

Short Solution Steps

Subtract 4 from -20 to get -24.

$$\frac{x\left(-24\right)}{x+10}-20-\frac{x\left(-20-x\right)}{x+40}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{x+10}{x+10}.

$$\frac{x\left(-24\right)}{x+10}-\frac{20\left(x+10\right)}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Since \frac{x\left(-24\right)}{x+10} and \frac{20\left(x+10\right)}{x+10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-24\right)-20\left(x+10\right)}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Do the multiplications in x\left(-24\right)-20\left(x+10\right).

$$\frac{x\left(-24\right)-20x-200}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Combine like terms in x\left(-24\right)-20x-200.

$$\frac{-44x-200}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+10 and x+40 is \left(x+10\right)\left(x+40\right). Multiply \frac{-44x-200}{x+10} times \frac{x+40}{x+40}. Multiply \frac{x\left(-20-x\right)}{x+40} times \frac{x+10}{x+10}.

$$\frac{\left(-44x-200\right)\left(x+40\right)}{\left(x+10\right)\left(x+40\right)}-\frac{x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)}$$

Since \frac{\left(-44x-200\right)\left(x+40\right)}{\left(x+10\right)\left(x+40\right)} and \frac{x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-44x-200\right)\left(x+40\right)-x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)}$$

Do the multiplications in \left(-44x-200\right)\left(x+40\right)-x\left(-20-x\right)\left(x+10\right).

$$\frac{-44x^{2}-1760x-200x-8000+20x^{2}+200x+x^{3}+10x^{2}}{\left(x+10\right)\left(x+40\right)}$$

Combine like terms in -44x^{2}-1760x-200x-8000+20x^{2}+200x+x^{3}+10x^{2}.

$$\frac{-14x^{2}-1760x-8000+x^{3}}{\left(x+10\right)\left(x+40\right)}$$

Expand \left(x+10\right)\left(x+40\right).

$$\frac{-14x^{2}-1760x-8000+x^{3}}{x^{2}+50x+400}$$

Expand

$$\frac{x^{3}-14x^{2}-1760x-8000}{\left(x+10\right)\left(x+40\right)}$$

Short Solution Steps

Subtract 4 from -20 to get -24.

$$\frac{x\left(-24\right)}{x+10}-20-\frac{x\left(-20-x\right)}{x+40}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{x+10}{x+10}.

$$\frac{x\left(-24\right)}{x+10}-\frac{20\left(x+10\right)}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Since \frac{x\left(-24\right)}{x+10} and \frac{20\left(x+10\right)}{x+10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-24\right)-20\left(x+10\right)}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Do the multiplications in x\left(-24\right)-20\left(x+10\right).

$$\frac{x\left(-24\right)-20x-200}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

Combine like terms in x\left(-24\right)-20x-200.

$$\frac{-44x-200}{x+10}-\frac{x\left(-20-x\right)}{x+40}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+10 and x+40 is \left(x+10\right)\left(x+40\right). Multiply \frac{-44x-200}{x+10} times \frac{x+40}{x+40}. Multiply \frac{x\left(-20-x\right)}{x+40} times \frac{x+10}{x+10}.

$$\frac{\left(-44x-200\right)\left(x+40\right)}{\left(x+10\right)\left(x+40\right)}-\frac{x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)}$$

Since \frac{\left(-44x-200\right)\left(x+40\right)}{\left(x+10\right)\left(x+40\right)} and \frac{x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-44x-200\right)\left(x+40\right)-x\left(-20-x\right)\left(x+10\right)}{\left(x+10\right)\left(x+40\right)}$$

Do the multiplications in \left(-44x-200\right)\left(x+40\right)-x\left(-20-x\right)\left(x+10\right).

$$\frac{-44x^{2}-1760x-200x-8000+20x^{2}+200x+x^{3}+10x^{2}}{\left(x+10\right)\left(x+40\right)}$$

Combine like terms in -44x^{2}-1760x-200x-8000+20x^{2}+200x+x^{3}+10x^{2}.

$$\frac{-14x^{2}-1760x-8000+x^{3}}{\left(x+10\right)\left(x+40\right)}$$

Expand \left(x+10\right)\left(x+40\right).

$$\frac{-14x^{2}-1760x-8000+x^{3}}{x^{2}+50x+400}$$