Solve 3x-7/(x-2)^2-5/x-2

$$\frac { 3 x - 7 } { ( x - 2 ) ^ { 2 } } - \frac { 5 } { x - 2 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{3x-7}{\left(x-2\right)^{2}}-\frac{5\left(x-2\right)}{\left(x-2\right)^{2}}$$

Since \frac{3x-7}{\left(x-2\right)^{2}} and \frac{5\left(x-2\right)}{\left(x-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x-7-5\left(x-2\right)}{\left(x-2\right)^{2}}$$

Do the multiplications in 3x-7-5\left(x-2\right).

$$\frac{3x-7-5x+10}{\left(x-2\right)^{2}}$$

Combine like terms in 3x-7-5x+10.

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

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

$$\frac{-2x+3}{x^{2}-4x+4}$$

Expand

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

Short Solution Steps

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

$$\frac{3x-7}{\left(x-2\right)^{2}}-\frac{5\left(x-2\right)}{\left(x-2\right)^{2}}$$

Since \frac{3x-7}{\left(x-2\right)^{2}} and \frac{5\left(x-2\right)}{\left(x-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x-7-5\left(x-2\right)}{\left(x-2\right)^{2}}$$

Do the multiplications in 3x-7-5\left(x-2\right).

$$\frac{3x-7-5x+10}{\left(x-2\right)^{2}}$$

Combine like terms in 3x-7-5x+10.

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

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

$$\frac{-2x+3}{x^{2}-4x+4}$$