# Rational Expressions Worksheet

Content type
User Generated
Subject
Mathematics
Type
Worksheet
Rating
Showing Page:
1/1
1.



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) * 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.



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.




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.

Unformatted Attachment Preview
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 − ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

### Review

Anonymous
I was having a hard time with this subject, and this was a great help.

Studypool
4.7
Indeed
4.5
Sitejabber
4.4