Solve x^2+25/(x-5)^3+10x/(5-x)^3

$$\frac { x ^ { 2 } + 25 } { ( x - 5 ) ^ { 3 } } + \frac { 10 x } { ( 5 - x ) ^ { 3 } }$$

Evaluate

$$\frac{1}{x-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)^{3} and \left(5-x\right)^{3} is \left(x-5\right)^{3}. Multiply \frac{10x}{\left(5-x\right)^{3}} times \frac{-1}{-1}.

$$\frac{x^{2}+25}{\left(x-5\right)^{3}}+\frac{-10x}{\left(x-5\right)^{3}}$$

Since \frac{x^{2}+25}{\left(x-5\right)^{3}} and \frac{-10x}{\left(x-5\right)^{3}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+25-10x}{\left(x-5\right)^{3}}$$

Factor the expressions that are not already factored in \frac{x^{2}+25-10x}{\left(x-5\right)^{3}}.

$$\frac{\left(x-5\right)^{2}}{\left(x-5\right)^{3}}$$

Cancel out \left(x-5\right)^{2} in both numerator and denominator.

$$\frac{1}{x-5}$$

Expand

$$\frac{1}{x-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)^{3} and \left(5-x\right)^{3} is \left(x-5\right)^{3}. Multiply \frac{10x}{\left(5-x\right)^{3}} times \frac{-1}{-1}.

$$\frac{x^{2}+25}{\left(x-5\right)^{3}}+\frac{-10x}{\left(x-5\right)^{3}}$$

Since \frac{x^{2}+25}{\left(x-5\right)^{3}} and \frac{-10x}{\left(x-5\right)^{3}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+25-10x}{\left(x-5\right)^{3}}$$

Factor the expressions that are not already factored in \frac{x^{2}+25-10x}{\left(x-5\right)^{3}}.

$$\frac{\left(x-5\right)^{2}}{\left(x-5\right)^{3}}$$

Cancel out \left(x-5\right)^{2} in both numerator and denominator.

$$\frac{1}{x-5}$$