Solve 8/w-7+54/(w-7)^2

$$\frac { 8 } { w - 7 } + \frac { 54 } { ( w - 7 ) ^ { 2 } }$$

Evaluate

$$\frac{2\left(4w-1\right)}{\left(w-7\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w-7 and \left(w-7\right)^{2} is \left(w-7\right)^{2}. Multiply \frac{8}{w-7} times \frac{w-7}{w-7}.

$$\frac{8\left(w-7\right)}{\left(w-7\right)^{2}}+\frac{54}{\left(w-7\right)^{2}}$$

Since \frac{8\left(w-7\right)}{\left(w-7\right)^{2}} and \frac{54}{\left(w-7\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{8\left(w-7\right)+54}{\left(w-7\right)^{2}}$$

Do the multiplications in 8\left(w-7\right)+54.

$$\frac{8w-56+54}{\left(w-7\right)^{2}}$$

Combine like terms in 8w-56+54.

$$\frac{8w-2}{\left(w-7\right)^{2}}$$

Expand \left(w-7\right)^{2}.

$$\frac{8w-2}{w^{2}-14w+49}$$

Expand

$$\frac{2\left(4w-1\right)}{\left(w-7\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w-7 and \left(w-7\right)^{2} is \left(w-7\right)^{2}. Multiply \frac{8}{w-7} times \frac{w-7}{w-7}.

$$\frac{8\left(w-7\right)}{\left(w-7\right)^{2}}+\frac{54}{\left(w-7\right)^{2}}$$

Since \frac{8\left(w-7\right)}{\left(w-7\right)^{2}} and \frac{54}{\left(w-7\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{8\left(w-7\right)+54}{\left(w-7\right)^{2}}$$

Do the multiplications in 8\left(w-7\right)+54.

$$\frac{8w-56+54}{\left(w-7\right)^{2}}$$

Combine like terms in 8w-56+54.

$$\frac{8w-2}{\left(w-7\right)^{2}}$$

Expand \left(w-7\right)^{2}.

$$\frac{8w-2}{w^{2}-14w+49}$$