How to add rational expressions with a common denominator

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PSAT Math › How to add rational expressions with a common denominator

Questions 1 - 3

1

Simplify.

$\frac{x^{2}-4}{2x+8}+\frac{-12}{2x+8}$

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

$\frac{x^{2}-16}{2x+8}$

$\frac{x-2}{6}$

$\frac{x^{2}-2}{2x}$

$\frac{x^{2}-16}{x+4}$

Explanation

$\frac{x^{2}-4}{2x+8}+\frac{-12}{2x+8}$

Check for same Denominator

$\frac{x^{2}-4+(-12)}{2x+8}$

Add like terms

$\frac{x^{2}-16}{2x+8}$

Check for GCF or if the expression can be factored

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

After factoring, divide out like terms.

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

Final Answer

2

Simplify the following rational expression: (9x - 2)/(x2) MINUS (6x - 8)/(x2)

$\frac{15x+6}{x}$

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

$\frac{12x-6}{x}$

Explanation

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

3

Simplify.

$\frac{2x+3}{x+2}+\frac{5x-6}{x+2}$

$\frac{7x-3}{x+2}$

$\frac{7x-3}{2x+4}$

$\frac{5x-1}{2}$

$\frac{7x+9}{2x+4}$

Explanation

$\frac{2x-3}{x+2}+\frac{5x-6}{x+2}$

Same denominator means you add straight across the numerators, keeping the denominator the same.

$\frac{2x-3+5x-6}{x+2}$

Add like terms.

$\frac{2x+5x+3-6}{x+2}$

Final Answer.

$\frac{7x-3}{x+2}$

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