Solve a^2-a-6/a^2-4-2-a-1/2-a=

$$\frac { a ^ { 2 } - a - 6 } { a ^ { 2 } - 4 } - 2 - \frac { a - 1 } { 2 - a } =$$

Evaluate

$$0$$

Short Solution Steps

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

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

Cancel out a+2 in both numerator and denominator.

$$\frac{a-3}{a-2}-2-\frac{a-1}{2-a}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{a-2}{a-2}.

$$\frac{a-3}{a-2}-\frac{2\left(a-2\right)}{a-2}-\frac{a-1}{2-a}$$

Since \frac{a-3}{a-2} and \frac{2\left(a-2\right)}{a-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-3-2\left(a-2\right)}{a-2}-\frac{a-1}{2-a}$$

Do the multiplications in a-3-2\left(a-2\right).

$$\frac{a-3-2a+4}{a-2}-\frac{a-1}{2-a}$$

Combine like terms in a-3-2a+4.

$$\frac{-a+1}{a-2}-\frac{a-1}{2-a}$$

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

$$\frac{-a+1}{a-2}-\frac{-\left(a-1\right)}{a-2}$$

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

$$\frac{-a+1-\left(-\left(a-1\right)\right)}{a-2}$$

Do the multiplications in -a+1-\left(-\left(a-1\right)\right).

$$\frac{-a+1+a-1}{a-2}$$

Combine like terms in -a+1+a-1.

$$\frac{0}{a-2}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$