Question

If the numerator and the denominator of a rational expression have a common factor, how would you simplify the expression? Simplify the expression$\frac{x^2+x}{x+1}$

Short answer

If the numerator and denominator have a common factor then cancel out the common terms from numerator and denominator, the value of the given expression is $x$.

Step-by-step solution

Step 1. Write the given information.

The given expression has a common term in both the numerator and the denominator.

Step 2. Procedure to simplify.

If the numerator and denominator of given rational expression have a common factor, then take common terms from both numerator and denominator and then cancel out the common factors in numerator and denominator.

Step 3. Simplify the expression.

The given expression is,

$\frac{x^2+x}{x+1}$

The above expression is simplified as,

$\begin{array}{c}\frac{x^2+x}{x+1}=\frac{x\left(x+1\right)}{\left(x+1\right)}\\ =x\end{array}$

Thus, if the numerator and denominator have a common factor then cancel out the common terms from numerator and denominator, the value of the given expression is $x$.