Question

Simplify the expression. $$\frac{x}{x+2} \div \frac{x+5}{x+2}$$

Short answer

The simplified form of the given expression is \(\frac{x}{x+5}\) where \(x \neq -5\).

Step-by-step solution

Change Division To Multiplication

The division of two fractions can be transformed into the multiplication by inverting the second fraction. So, the expression \(\frac{x}{x+2} \div \frac{x+5}{x+2}\) would become \(\frac{x}{x+2} * \frac{x+2}{x+5}\). In this step, the reciprocal of the divisor \(\frac{x+5}{x+2}\) is calculated, which is \(\frac{x+2}{x+5}\). After that, the initial division operation is changed to multiplication.

Simplify

Next, cancel the common factors in the numerator and the denominator. Here the term \((x+2)\) is common to both numerator and denominator. After canceling out, the expression becomes \(\frac{x}{x+5}\).

Check

Always remember to check the domain of the expression. Here the denominator shouldn't be zero, therefore \(x \neq -5\).