Solve 64-2ab/(a-8)^2+2ab-a^2/(8-a)^2

$$\frac { 64 - 2 a b } { ( a - 8 ) ^ { 2 } } + \frac { 2 a b - a ^ { 2 } } { ( 8 - a ) ^ { 2 } }$$

Evaluate

$$\frac{a+8}{8-a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Expand \left(8-a\right)^{2}.

$$\frac{64-2ab}{\left(a-8\right)^{2}}+\frac{2ab-a^{2}}{\left(a-8\right)^{2}}$$

Since \frac{64-2ab}{\left(a-8\right)^{2}} and \frac{2ab-a^{2}}{\left(a-8\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{64-2ab+2ab-a^{2}}{\left(a-8\right)^{2}}$$

Combine like terms in 64-2ab+2ab-a^{2}.

$$\frac{64-a^{2}}{\left(a-8\right)^{2}}$$

Factor the expressions that are not already factored in \frac{64-a^{2}}{\left(a-8\right)^{2}}.

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

Cancel out a-8 in both numerator and denominator.

$$\frac{-a-8}{a-8}$$

Expand

$$-\frac{a+8}{a-8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Expand \left(8-a\right)^{2}.

$$\frac{64-2ab}{\left(a-8\right)^{2}}+\frac{2ab-a^{2}}{\left(a-8\right)^{2}}$$

Since \frac{64-2ab}{\left(a-8\right)^{2}} and \frac{2ab-a^{2}}{\left(a-8\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{64-2ab+2ab-a^{2}}{\left(a-8\right)^{2}}$$

Combine like terms in 64-2ab+2ab-a^{2}.

$$\frac{64-a^{2}}{\left(a-8\right)^{2}}$$

Factor the expressions that are not already factored in \frac{64-a^{2}}{\left(a-8\right)^{2}}.

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

Cancel out a-8 in both numerator and denominator.

$$\frac{-a-8}{a-8}$$