Solve y-4/y^2-4-6-y/4-y^2

$$\frac { y - 4 } { y ^ { 2 } - 4 } - \frac { 6 - y } { 4 - y ^ { 2 } }$$

Evaluate

$$\frac{2}{y^{2}-4}$$

Short Solution Steps

Factor y^{2}-4. Factor 4-y^{2}.

$$\frac{y-4}{\left(y-2\right)\left(y+2\right)}-\frac{6-y}{\left(y-2\right)\left(-y-2\right)}$$

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

$$\frac{y-4}{\left(y-2\right)\left(y+2\right)}-\frac{-\left(6-y\right)}{\left(y-2\right)\left(y+2\right)}$$

Since \frac{y-4}{\left(y-2\right)\left(y+2\right)} and \frac{-\left(6-y\right)}{\left(y-2\right)\left(y+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y-4-\left(-\left(6-y\right)\right)}{\left(y-2\right)\left(y+2\right)}$$

Do the multiplications in y-4-\left(-\left(6-y\right)\right).

$$\frac{y-4+6-y}{\left(y-2\right)\left(y+2\right)}$$

Combine like terms in y-4+6-y.

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

Expand \left(y-2\right)\left(y+2\right).

$$\frac{2}{y^{2}-4}$$

Expand

$$\frac{2}{y^{2}-4}$$

Short Solution Steps

Factor y^{2}-4. Factor 4-y^{2}.

$$\frac{y-4}{\left(y-2\right)\left(y+2\right)}-\frac{6-y}{\left(y-2\right)\left(-y-2\right)}$$

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

$$\frac{y-4}{\left(y-2\right)\left(y+2\right)}-\frac{-\left(6-y\right)}{\left(y-2\right)\left(y+2\right)}$$

Since \frac{y-4}{\left(y-2\right)\left(y+2\right)} and \frac{-\left(6-y\right)}{\left(y-2\right)\left(y+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y-4-\left(-\left(6-y\right)\right)}{\left(y-2\right)\left(y+2\right)}$$

Do the multiplications in y-4-\left(-\left(6-y\right)\right).

$$\frac{y-4+6-y}{\left(y-2\right)\left(y+2\right)}$$

Combine like terms in y-4+6-y.

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

Expand \left(y-2\right)\left(y+2\right).

$$\frac{2}{y^{2}-4}$$