Question

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{6 x}{x+1}-\frac{2 x+4}{x+1}$$

Short answer

The simplified expression is \(\frac{x - 1}{x+1}\).

Step-by-step solution

Understand the problem and set up the expression

We are given the rational expression \(\frac{6x}{x+1} - \frac{2x+4}{x+1}\), since they have the same denominator we can combine them under one fraction.

Combine fractions

We can subtract the two fractions by subtracting the numerators, we get \(\frac{6x - (2x + 4)}{x+1}\).

Simplify the numerator

Expand the expression in the numerator \(6x - 2x - 4\), you get \(4x - 4\).

Final simplification

Finally, divide both terms in the numerator by 4 to simplify the expression, so we get \(\frac{x - 1}{x+1}\).