Solve a/p-3a-a/p

$$\frac { a } { p - 3 a } - \frac { a } { p }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p-3a and p is p\left(p-3a\right). Multiply \frac{a}{p-3a} times \frac{p}{p}. Multiply \frac{a}{p} times \frac{p-3a}{p-3a}.

$$\frac{ap}{p\left(p-3a\right)}-\frac{a\left(p-3a\right)}{p\left(p-3a\right)}$$

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

$$\frac{ap-a\left(p-3a\right)}{p\left(p-3a\right)}$$

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

$$\frac{ap-ap+3a^{2}}{p\left(p-3a\right)}$$

Combine like terms in ap-ap+3a^{2}.

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

Expand p\left(p-3a\right).

$$\frac{3a^{2}}{p^{2}-3ap}$$

Factor

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