Solve 3/p+3r-p-15r/p^2-9r^2

$$\frac { 3 } { p + 3 r } - \frac { p - 15 r } { p ^ { 2 } - 9 r ^ { 2 } }$$

Evaluate

$$\frac{2}{p-3r}$$

Short Solution Steps

Factor p^{2}-9r^{2}.

$$\frac{3}{p+3r}-\frac{p-15r}{\left(p-3r\right)\left(p+3r\right)}$$

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

$$\frac{3\left(p-3r\right)}{\left(p-3r\right)\left(p+3r\right)}-\frac{p-15r}{\left(p-3r\right)\left(p+3r\right)}$$

Since \frac{3\left(p-3r\right)}{\left(p-3r\right)\left(p+3r\right)} and \frac{p-15r}{\left(p-3r\right)\left(p+3r\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(p-3r\right)-\left(p-15r\right)}{\left(p-3r\right)\left(p+3r\right)}$$

Do the multiplications in 3\left(p-3r\right)-\left(p-15r\right).

$$\frac{3p-9r-p+15r}{\left(p-3r\right)\left(p+3r\right)}$$

Combine like terms in 3p-9r-p+15r.

$$\frac{2p+6r}{\left(p-3r\right)\left(p+3r\right)}$$

Factor the expressions that are not already factored in \frac{2p+6r}{\left(p-3r\right)\left(p+3r\right)}.

$$\frac{2\left(p+3r\right)}{\left(p-3r\right)\left(p+3r\right)}$$

Cancel out p+3r in both numerator and denominator.

$$\frac{2}{p-3r}$$

Expand

$$\frac{6}{3p-9r}$$

Short Solution Steps

Factor p^{2}-9r^{2}.

$$\frac{3}{p+3r}-\frac{p-15r}{\left(p-3r\right)\left(p+3r\right)}$$

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

$$\frac{3\left(p-3r\right)}{\left(p-3r\right)\left(p+3r\right)}-\frac{p-15r}{\left(p-3r\right)\left(p+3r\right)}$$

Since \frac{3\left(p-3r\right)}{\left(p-3r\right)\left(p+3r\right)} and \frac{p-15r}{\left(p-3r\right)\left(p+3r\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(p-3r\right)-\left(p-15r\right)}{\left(p-3r\right)\left(p+3r\right)}$$

Do the multiplications in 3\left(p-3r\right)-\left(p-15r\right).

$$\frac{3p-9r-p+15r}{\left(p-3r\right)\left(p+3r\right)}$$

Combine like terms in 3p-9r-p+15r.

$$\frac{2p+6r}{\left(p-3r\right)\left(p+3r\right)}$$

Factor the expressions that are not already factored in \frac{2p+6r}{\left(p-3r\right)\left(p+3r\right)}.

$$\frac{2\left(p+3r\right)}{\left(p-3r\right)\left(p+3r\right)}$$

Cancel out p+3r in both numerator and denominator.

$$\frac{2}{p-3r}$$