Solve 16/4a-a^2-4/a

$$\frac { 16 } { 4 a - a ^ { 2 } } - \frac { 4 } { a }$$

Evaluate

$$\frac{4}{4-a}$$

Short Solution Steps

Factor 4a-a^{2}.

$$\frac{16}{a\left(-a+4\right)}-\frac{4}{a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(-a+4\right) and a is a\left(-a+4\right). Multiply \frac{4}{a} times \frac{-a+4}{-a+4}.

$$\frac{16}{a\left(-a+4\right)}-\frac{4\left(-a+4\right)}{a\left(-a+4\right)}$$

Since \frac{16}{a\left(-a+4\right)} and \frac{4\left(-a+4\right)}{a\left(-a+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-4\left(-a+4\right)}{a\left(-a+4\right)}$$

Do the multiplications in 16-4\left(-a+4\right).

$$\frac{16+4a-16}{a\left(-a+4\right)}$$

Combine like terms in 16+4a-16.

$$\frac{4a}{a\left(-a+4\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{4}{-a+4}$$

Factor

$$\frac{4}{4-a}$$