How to add rational expressions with different denominators

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PSAT Math › How to add rational expressions with different denominators

Questions 1 - 1

Simplify the expression.

$\frac{x}{2x+4}+\frac{x}{x+2}$

$\frac{2x}{3x+6}$

$\frac{3x}{2x+4}$

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

$\frac{1}{2x+4}$

$\frac{x+1}{2x+4}$

Explanation

To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.

$\frac{x}{2x+4}+\frac{x}{x+2}$

$\frac{x}{2x+4}+\frac{(2)x}{(2)(x+2)}$

$\frac{x}{2x+4}+\frac{2x}{2x+4}$

$\frac{3x}{2x+4}$

This is the most simplified version of the rational expression.

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