Solve 3/x-5-1/(x-5)^2

$$\frac { 3 } { x - 5 } - \frac { 1 } { ( x - 5 ) ^ { 2 } }$$

Evaluate

$$\frac{3x-16}{\left(x-5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-5 and \left(x-5\right)^{2} is \left(x-5\right)^{2}. Multiply \frac{3}{x-5} times \frac{x-5}{x-5}.

$$\frac{3\left(x-5\right)}{\left(x-5\right)^{2}}-\frac{1}{\left(x-5\right)^{2}}$$

Since \frac{3\left(x-5\right)}{\left(x-5\right)^{2}} and \frac{1}{\left(x-5\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x-5\right)-1}{\left(x-5\right)^{2}}$$

Do the multiplications in 3\left(x-5\right)-1.

$$\frac{3x-15-1}{\left(x-5\right)^{2}}$$

Combine like terms in 3x-15-1.

$$\frac{3x-16}{\left(x-5\right)^{2}}$$

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

$$\frac{3x-16}{x^{2}-10x+25}$$

Expand

$$\frac{3x-16}{\left(x-5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-5 and \left(x-5\right)^{2} is \left(x-5\right)^{2}. Multiply \frac{3}{x-5} times \frac{x-5}{x-5}.

$$\frac{3\left(x-5\right)}{\left(x-5\right)^{2}}-\frac{1}{\left(x-5\right)^{2}}$$

Since \frac{3\left(x-5\right)}{\left(x-5\right)^{2}} and \frac{1}{\left(x-5\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x-5\right)-1}{\left(x-5\right)^{2}}$$

Do the multiplications in 3\left(x-5\right)-1.

$$\frac{3x-15-1}{\left(x-5\right)^{2}}$$

Combine like terms in 3x-15-1.

$$\frac{3x-16}{\left(x-5\right)^{2}}$$

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

$$\frac{3x-16}{x^{2}-10x+25}$$