Solve 4a-ab/3a+16-b^2/15

$$\frac { 4 a - a b } { 3 a } + \frac { 16 - b ^ { 2 } } { 15 }$$

Evaluate

$$\frac{\left(4-b\right)\left(b+9\right)}{15}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4a-ab}{3a}.

$$\frac{a\left(-b+4\right)}{3a}+\frac{16-b^{2}}{15}$$

Cancel out a in both numerator and denominator.

$$\frac{-b+4}{3}+\frac{16-b^{2}}{15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 15 is 15. Multiply \frac{-b+4}{3} times \frac{5}{5}.

$$\frac{5\left(-b+4\right)}{15}+\frac{16-b^{2}}{15}$$

Since \frac{5\left(-b+4\right)}{15} and \frac{16-b^{2}}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\left(-b+4\right)+16-b^{2}}{15}$$

Do the multiplications in 5\left(-b+4\right)+16-b^{2}.

$$\frac{-5b+20+16-b^{2}}{15}$$

Combine like terms in -5b+20+16-b^{2}.

$$\frac{-5b+36-b^{2}}{15}$$

Expand

$$-\frac{b^{2}}{15}-\frac{b}{3}+\frac{12}{5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4a-ab}{3a}.

$$\frac{a\left(-b+4\right)}{3a}+\frac{16-b^{2}}{15}$$

Cancel out a in both numerator and denominator.

$$\frac{-b+4}{3}+\frac{16-b^{2}}{15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 15 is 15. Multiply \frac{-b+4}{3} times \frac{5}{5}.

$$\frac{5\left(-b+4\right)}{15}+\frac{16-b^{2}}{15}$$

Since \frac{5\left(-b+4\right)}{15} and \frac{16-b^{2}}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\left(-b+4\right)+16-b^{2}}{15}$$

Do the multiplications in 5\left(-b+4\right)+16-b^{2}.

$$\frac{-5b+20+16-b^{2}}{15}$$

Combine like terms in -5b+20+16-b^{2}.

$$\frac{-5b+36-b^{2}}{15}$$