Solve 6p/p^2-6p+9+5/6

$$\frac { 6 p } { p ^ { 2 } - 6 p + 9 } + \frac { 5 } { 6 }$$

Evaluate

$$\frac{5p^{2}+6p+45}{6\left(p-3\right)^{2}}$$

Short Solution Steps

Factor p^{2}-6p+9.

$$\frac{6p}{\left(p-3\right)^{2}}+\frac{5}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p-3\right)^{2} and 6 is 6\left(p-3\right)^{2}. Multiply \frac{6p}{\left(p-3\right)^{2}} times \frac{6}{6}. Multiply \frac{5}{6} times \frac{\left(p-3\right)^{2}}{\left(p-3\right)^{2}}.

$$\frac{6\times 6p}{6\left(p-3\right)^{2}}+\frac{5\left(p-3\right)^{2}}{6\left(p-3\right)^{2}}$$

Since \frac{6\times 6p}{6\left(p-3\right)^{2}} and \frac{5\left(p-3\right)^{2}}{6\left(p-3\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{6\times 6p+5\left(p-3\right)^{2}}{6\left(p-3\right)^{2}}$$

Do the multiplications in 6\times 6p+5\left(p-3\right)^{2}.

$$\frac{36p+5p^{2}-30p+45}{6\left(p-3\right)^{2}}$$

Combine like terms in 36p+5p^{2}-30p+45.

$$\frac{6p+5p^{2}+45}{6\left(p-3\right)^{2}}$$

Expand 6\left(p-3\right)^{2}.

$$\frac{6p+5p^{2}+45}{6p^{2}-36p+54}$$

Factor

$$\frac{5p^{2}+6p+45}{6\left(p-3\right)^{2}}$$