Solve 36/4a-a^2-9/a

$$\frac { 36 } { 4 a - a ^ { 2 } } - \frac { 9 } { a }$$

Evaluate

$$\frac{9}{4-a}$$

Short Solution Steps

Factor 4a-a^{2}.

$$\frac{36}{a\left(-a+4\right)}-\frac{9}{a}$$

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{9}{a} times \frac{-a+4}{-a+4}.

$$\frac{36}{a\left(-a+4\right)}-\frac{9\left(-a+4\right)}{a\left(-a+4\right)}$$

Since \frac{36}{a\left(-a+4\right)} and \frac{9\left(-a+4\right)}{a\left(-a+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-9\left(-a+4\right)}{a\left(-a+4\right)}$$

Do the multiplications in 36-9\left(-a+4\right).

$$\frac{36+9a-36}{a\left(-a+4\right)}$$

Combine like terms in 36+9a-36.

$$\frac{9a}{a\left(-a+4\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{9}{-a+4}$$

Factor

$$\frac{9}{4-a}$$