Solve 5x/x^2-7x+6-2(x+2)/x^2-4x-12

$$\frac { 5 x } { x ^ { 2 } - 7 x + 6 } - \frac { 2 ( x + 2 ) } { x ^ { 2 } - 4 x - 12 }$$

Evaluate

$$\frac{3x+2}{\left(x-6\right)\left(x-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2\left(x+2\right)}{x^{2}-4x-12}.

$$\frac{5x}{x^{2}-7x+6}-\frac{2\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{5x}{x^{2}-7x+6}-\frac{2}{x-6}$$

Factor x^{2}-7x+6.

$$\frac{5x}{\left(x-6\right)\left(x-1\right)}-\frac{2}{x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x-1\right) and x-6 is \left(x-6\right)\left(x-1\right). Multiply \frac{2}{x-6} times \frac{x-1}{x-1}.

$$\frac{5x}{\left(x-6\right)\left(x-1\right)}-\frac{2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)}$$

Since \frac{5x}{\left(x-6\right)\left(x-1\right)} and \frac{2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)}$$

Do the multiplications in 5x-2\left(x-1\right).

$$\frac{5x-2x+2}{\left(x-6\right)\left(x-1\right)}$$

Combine like terms in 5x-2x+2.

$$\frac{3x+2}{\left(x-6\right)\left(x-1\right)}$$

Expand \left(x-6\right)\left(x-1\right).

$$\frac{3x+2}{x^{2}-7x+6}$$

Expand

$$\frac{3x+2}{\left(x-6\right)\left(x-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2\left(x+2\right)}{x^{2}-4x-12}.

$$\frac{5x}{x^{2}-7x+6}-\frac{2\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{5x}{x^{2}-7x+6}-\frac{2}{x-6}$$

Factor x^{2}-7x+6.

$$\frac{5x}{\left(x-6\right)\left(x-1\right)}-\frac{2}{x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x-1\right) and x-6 is \left(x-6\right)\left(x-1\right). Multiply \frac{2}{x-6} times \frac{x-1}{x-1}.

$$\frac{5x}{\left(x-6\right)\left(x-1\right)}-\frac{2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)}$$

Since \frac{5x}{\left(x-6\right)\left(x-1\right)} and \frac{2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2\left(x-1\right)}{\left(x-6\right)\left(x-1\right)}$$

Do the multiplications in 5x-2\left(x-1\right).

$$\frac{5x-2x+2}{\left(x-6\right)\left(x-1\right)}$$

Combine like terms in 5x-2x+2.

$$\frac{3x+2}{\left(x-6\right)\left(x-1\right)}$$

Expand \left(x-6\right)\left(x-1\right).

$$\frac{3x+2}{x^{2}-7x+6}$$