Solve 3/(x-4)^2-1/(4-x)

$$\frac { 3 } { ( x - 4 ) ^ { 2 } } - \frac { 1 } { ( 4 - x ) }$$

Evaluate

$$-\frac{1-x}{\left(4-x\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)^{2} and 4-x is \left(x-4\right)^{2}. Multiply \frac{1}{4-x} times \frac{-\left(x-4\right)}{-\left(x-4\right)}.

$$\frac{3}{\left(x-4\right)^{2}}-\frac{-\left(x-4\right)}{\left(x-4\right)^{2}}$$

Since \frac{3}{\left(x-4\right)^{2}} and \frac{-\left(x-4\right)}{\left(x-4\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-\left(-\left(x-4\right)\right)}{\left(x-4\right)^{2}}$$

Do the multiplications in 3-\left(-\left(x-4\right)\right).

$$\frac{3+x-4}{\left(x-4\right)^{2}}$$

Combine like terms in 3+x-4.

$$\frac{-1+x}{\left(x-4\right)^{2}}$$

Expand \left(x-4\right)^{2}.

$$\frac{-1+x}{x^{2}-8x+16}$$

Expand

$$-\frac{1-x}{\left(x-4\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)^{2} and 4-x is \left(x-4\right)^{2}. Multiply \frac{1}{4-x} times \frac{-\left(x-4\right)}{-\left(x-4\right)}.

$$\frac{3}{\left(x-4\right)^{2}}-\frac{-\left(x-4\right)}{\left(x-4\right)^{2}}$$

Since \frac{3}{\left(x-4\right)^{2}} and \frac{-\left(x-4\right)}{\left(x-4\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-\left(-\left(x-4\right)\right)}{\left(x-4\right)^{2}}$$

Do the multiplications in 3-\left(-\left(x-4\right)\right).

$$\frac{3+x-4}{\left(x-4\right)^{2}}$$

Combine like terms in 3+x-4.

$$\frac{-1+x}{\left(x-4\right)^{2}}$$

Expand \left(x-4\right)^{2}.

$$\frac{-1+x}{x^{2}-8x+16}$$