Question

Simplify the fraction. $$\frac{5 x y}{5 x^{2}}$$

Short answer

The simplified form of the fraction is \(\frac{y}{x}\).

Step-by-step solution

Identify common factors in the numerator and the denominator

Notice the common factor of \(5\) and \(x\) in both the numerator \(5xy\) and the denominator \(5x^2\). Identify these common factors for cancelation.

Cancel the common factors

Remove the common factors from both the numerator and the denominator. This is equivalent to dividing both the numerator and the denominator by those factors. So you have \(\frac{(5xy)/(5x)}{(5x^2)/(5x)}\).

Simplify the fraction

After dividing both parts of the fractions by the common factor, \(y\) remains in the numerator and \(x\) remains in the denominator. Thus, the simplified form of the given fraction is \(\frac{y}{x}\).