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Simplifying Rational Expressions (Grades 11-12)

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Simplifying Rational Expressions

1. 
To simplify the rational expression [math](x+6)/(x^2+5x-6[/math], what is the factored form of the trinomial in the denominator?
  1. [math](x+6)(x-1)[/math]
  2. [math](x-6)(x+1)[/math]
  3. [math](x-6)(x-1)[/math]
  4. [math](x+6)(x+1)[/math]
2. 
Find the value that makes the rational expression undefined:

[math]8/(y+6)[/math]
  1. [math]y= -4[/math]
  2. [math]y=0[/math]
  3. [math]y=3[/math]
  4. [math]y=-6[/math]
3. 
Find the values that make the rational expression undefined:

[math](x^2+3)/(x(x+5)[/math]
  1. [math]x=0[/math] or [math]-5[/math]
  2. [math]x=0[/math] or [math]7[/math]
  3. [math]x=0[/math] or [math]5[/math]
  4. [math]x=2[/math] or [math]4[/math]
4. 
Simplify the expression [math](x-7)/(x^2-x-42)[/math].
  1. [math]1/(x+7), \ x!=-6[/math]
  2. [math]1/(x+6), \ x!= 7[/math]
  3. [math]x+7, \ x!= -6, 7[/math]
  4. [math]x+6, \ x!= -6, 7[/math]
5. 
Simplify. [math](x - y)/(x^2 - 2xy + y^2)[/math]
  1. [math]x + y[/math]
  2. [math]xy[/math]
  3. [math]1/(x-y)[/math]
  4. [math]x - y[/math]
6. 
Simplify. [math](a - 1)/[(a)^2-1][/math]
  1. [math]1/a, \ a!=0[/math]
  2. [math]1/(a - 1), \ a!= -1[/math]
  3. [math]1/(1- a), \ a!=1 [/math]
  4. [math]1/(a + 1), \ a!=1[/math]
7. 
Simplify the expression [math](7x^2-63)/(x+3)[/math].
  1. [math](x+3)/7, \ x!=-3[/math]
  2. [math](7x^2-9)/(x), \ x!=-3[/math]
  3. [math]7(x+3), \ x!=-3[/math]
  4. [math]7(x-3), \ x!=-3[/math]
8. 
Simplify. [math](5x + 7y)/( 3(x + y))[/math]
  1. [math]3[/math]
  2. [math]28/3[/math]
  3. [math]-1[/math]
  4. No further simplification
9. 
Simplify. [math](x^2y-x^5y^7+x^8y^4)/(x^2y)[/math]
  1. [math]1-x^3y^6+x^6y^3, \ \ \ \ x,y!=0[/math]
  2. [math]x^4y^2-x^7y^8+x^10y^5, \ \ \ \ x,y!=0[/math]
  3. [math]x^6y^3-x^3y^6-1, \ \ \ \ x,y!=0[/math]
  4. [math]xy-x^3y^6+x^6y^3, \ \ \ \ x,y!=0[/math]
10. 
Simplify. [math]((x^2-y^2)/(y^2-49))/((y-x)/(y+7))[/math]
  1. [math](y-x)/(y-7), \ x!=y, y!=-7[/math]
  2. [math](-x+y)/(y-7), \ x!=y, y!= -7[/math]
  3. [math](-x-y)/(-y-7), \ x!=y, y!=7[/math]
  4. [math](-x-y)/(y-7), \ x!=y, y!=-7[/math]
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