Solve 1/5-x+x-2/(x-5)^2=

$$\frac { 1 } { 5 - x } + \frac { x - 2 } { ( x - 5 ) ^ { 2 } } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-x and \left(x-5\right)^{2} is \left(x-5\right)^{2}. Multiply \frac{1}{5-x} times \frac{-\left(x-5\right)}{-\left(x-5\right)}.

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

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

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

Do the multiplications in -\left(x-5\right)+x-2.

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

Combine like terms in -x+5+x-2.

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

Expand \left(x-5\right)^{2}.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-x and \left(x-5\right)^{2} is \left(x-5\right)^{2}. Multiply \frac{1}{5-x} times \frac{-\left(x-5\right)}{-\left(x-5\right)}.

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

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

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

Do the multiplications in -\left(x-5\right)+x-2.

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

Combine like terms in -x+5+x-2.

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

Expand \left(x-5\right)^{2}.

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