Question

Simplify the expression. $$\frac{5 x}{x+4}+\frac{20}{4+x}$$

Short answer

The simplified expression is \(\frac{5x + 20}{x + 4}\)

Step-by-step solution

Identify the common denominator

In this case, both terms have the same denominator, \(x + 4\). So, it is the common denominator of the two terms.

Combine the fractions

As we have a common denominator, we can simply add the numerators. To do so, add \(5x\) and \(20\), thus getting \(5x + 20\).

Write the resulting fraction

Now, ccombine the numerators into a single term and keep the denominator as \(x + 4\). The result is \(\frac{5x + 20}{x + 4}\).