Solve x-10/x^2+3x-10-2x+4/x^2-4=

$$\frac { x - 10 } { x ^ { 2 } + 3 x - 10 } - \frac { 2 x + 4 } { x ^ { 2 } - 4 } =$$

Evaluate

$$-\frac{x+20}{\left(x-2\right)\left(x+5\right)}$$

Short Solution Steps

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

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x-10}{x^{2}+3x-10}-\frac{2}{x-2}$$

Factor x^{2}+3x-10.

$$\frac{x-10}{\left(x-2\right)\left(x+5\right)}-\frac{2}{x-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+5\right) and x-2 is \left(x-2\right)\left(x+5\right). Multiply \frac{2}{x-2} times \frac{x+5}{x+5}.

$$\frac{x-10}{\left(x-2\right)\left(x+5\right)}-\frac{2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Since \frac{x-10}{\left(x-2\right)\left(x+5\right)} and \frac{2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-10-2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Do the multiplications in x-10-2\left(x+5\right).

$$\frac{x-10-2x-10}{\left(x-2\right)\left(x+5\right)}$$

Combine like terms in x-10-2x-10.

$$\frac{-x-20}{\left(x-2\right)\left(x+5\right)}$$

Expand \left(x-2\right)\left(x+5\right).

$$\frac{-x-20}{x^{2}+3x-10}$$

Expand

$$-\frac{x+20}{\left(x-2\right)\left(x+5\right)}$$

Short Solution Steps

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

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x-10}{x^{2}+3x-10}-\frac{2}{x-2}$$

Factor x^{2}+3x-10.

$$\frac{x-10}{\left(x-2\right)\left(x+5\right)}-\frac{2}{x-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+5\right) and x-2 is \left(x-2\right)\left(x+5\right). Multiply \frac{2}{x-2} times \frac{x+5}{x+5}.

$$\frac{x-10}{\left(x-2\right)\left(x+5\right)}-\frac{2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Since \frac{x-10}{\left(x-2\right)\left(x+5\right)} and \frac{2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-10-2\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Do the multiplications in x-10-2\left(x+5\right).

$$\frac{x-10-2x-10}{\left(x-2\right)\left(x+5\right)}$$

Combine like terms in x-10-2x-10.

$$\frac{-x-20}{\left(x-2\right)\left(x+5\right)}$$

Expand \left(x-2\right)\left(x+5\right).

$$\frac{-x-20}{x^{2}+3x-10}$$