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Rational Expressions Worksheet

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1.
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x(x+5)/(x+3)(x+5) (x+2)(x+3)/(x+3)(x+5) x(x+5)+(x+2)(x+3)/(x+3)(x+5)
So x≠ -3, x≠ -5
The sum of this rational expression is rational expression because the sum will always equal
x*x+5 x+3*x+2/ x+3*x+5
2.
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x+4/(x+3)(x+2) * x+3/(x+4)(x-4) 1/(x+2)*1/(x-4) 1/(x+2)(x-4)
So x≠ -2, x≠ 4
The product of rational expressions is a rational expression because the product will always end
up as x+4*x+3/x^2+5x+6*x^2-16
3.
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2/(x+3)(x-3) 3x/(x-3)(x-2) 2(x-2)/(x+3)(x-3)(x-2) 3x(x+3)/(x+3)(x-3)(x-2) 2x-4-3x^2-
9x/(x+3)(x-3)(x-2) -3x^2-7x-4/(x+3)(x-3)(x-2) -1(3x+4)(x+1)/(x+3)(x-3)(x-2)
So x≠ -3, x≠ 3, x≠2, x≠0
The difference of rational expressions is a rational expression so 2*x^2-5x+6 x^2-9*3x
4.
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x+4/(x-2)(x-3) ÷ (x+4)(x-4)/x+3 (x+4)(x-4)/x+3 x+4/(x-2)(x-3) ÷ x+3/(x+4)(x-4) 1/(x-2)(x-3)
* x+3/x-4 x+3/(x-2)(x-3)(x-4)
So x≠ 2, x≠ 3, x≠ 4
The quotient of rational expressions is a rational expression (as long as the denominator is non-
zero).
5. Compare and contrast division of integers to division of rational expressions.
Dividing with integers and dividing with rational are similar but Closure does not apply to
division of integers since dividing integers can produce a fraction, which is not an integer. For
rational expression a fraction whose numerator and denominator are polynomials. Just as
addition, subtraction, and multiplication are closed on integers, they are closed for rational
expressions as well, with the addition of division since the division of rational expressions also
yields a rational expression.

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1. 𝑥 𝑥+3 𝑥+2 + 𝑥+5 x(x+5)/(x+3)(x+5) → (x+2)(x+3)/(x+3)(x+5) → x(x+5)+(x+2)(x+3)/(x+3)(x+5) So x≠ -3, x≠ -5 The sum of this rational expression is rational expression because the sum will always equal x*x+5 – x+3*x+2/ x+3*x+5 2. 𝑥+4 𝑥+3 ∗ 𝑥 2+ 5𝑥+6 𝑥 2 − ...
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I was having a hard time with this subject, and this was a great help.

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