Solve 5/w-4+19/(w-4)^2

$$\frac { 5 } { w - 4 } + \frac { 19 } { ( w - 4 ) ^ { 2 } }$$

Evaluate

$$\frac{5w-1}{\left(w-4\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w-4 and \left(w-4\right)^{2} is \left(w-4\right)^{2}. Multiply \frac{5}{w-4} times \frac{w-4}{w-4}.

$$\frac{5\left(w-4\right)}{\left(w-4\right)^{2}}+\frac{19}{\left(w-4\right)^{2}}$$

Since \frac{5\left(w-4\right)}{\left(w-4\right)^{2}} and \frac{19}{\left(w-4\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5\left(w-4\right)+19}{\left(w-4\right)^{2}}$$

Do the multiplications in 5\left(w-4\right)+19.

$$\frac{5w-20+19}{\left(w-4\right)^{2}}$$

Combine like terms in 5w-20+19.

$$\frac{5w-1}{\left(w-4\right)^{2}}$$

Expand \left(w-4\right)^{2}.

$$\frac{5w-1}{w^{2}-8w+16}$$

Expand

$$\frac{5w-1}{\left(w-4\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w-4 and \left(w-4\right)^{2} is \left(w-4\right)^{2}. Multiply \frac{5}{w-4} times \frac{w-4}{w-4}.

$$\frac{5\left(w-4\right)}{\left(w-4\right)^{2}}+\frac{19}{\left(w-4\right)^{2}}$$

Since \frac{5\left(w-4\right)}{\left(w-4\right)^{2}} and \frac{19}{\left(w-4\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5\left(w-4\right)+19}{\left(w-4\right)^{2}}$$

Do the multiplications in 5\left(w-4\right)+19.

$$\frac{5w-20+19}{\left(w-4\right)^{2}}$$

Combine like terms in 5w-20+19.

$$\frac{5w-1}{\left(w-4\right)^{2}}$$

Expand \left(w-4\right)^{2}.

$$\frac{5w-1}{w^{2}-8w+16}$$