Solve 1/x+4-1/x+3=

$$\frac { 1 } { x + 4 } - \frac { 1 } { x + 3 } =$$

Evaluate

$$-\frac{1}{\left(x+3\right)\left(x+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and x+3 is \left(x+3\right)\left(x+4\right). Multiply \frac{1}{x+4} times \frac{x+3}{x+3}. Multiply \frac{1}{x+3} times \frac{x+4}{x+4}.

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

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

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

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

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

Combine like terms in x+3-x-4.

$$\frac{-1}{\left(x+3\right)\left(x+4\right)}$$

Expand \left(x+3\right)\left(x+4\right).

$$\frac{-1}{x^{2}+7x+12}$$

Differentiate w.r.t. x

$$\frac{2x+7}{\left(\left(x+3\right)\left(x+4\right)\right)^{2}}$$