Radical and Rational Equations (Grades 11-12)

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Radical and Rational Equations

1. 
Solve for all possible values of [math]x[/math]: [math](6x-12)/(x-2)=6-x[/math]
  1. 0
  2. 2, 12
  3. 2, 0
  4. No Solution
2. 
Solve for all possible values of [math]x[/math]: [math]sqrt(x^2-3x+2)=sqrt(42)[/math]
  1. -3, 2
  2. No Solution
  3. 8, -5
  4. -5, 8
3. 
Solve for all possible values of [math]x[/math]: [math]sqrt(x+2)=sqrt(x)+2[/math]
  1. No Solution
  2. [math](7+-sqrt66)/4[/math]
  3. All real numbers
  4. [math](-7+-sqrt33)/4[/math]
4. 
Solve for all possible values of [math]x[/math]: [math]x/sqrtx=sqrtx[/math]
  1. All real numbers
  2. [math]x>=sqrtx[/math]
  3. [math]x>0[/math]
  4. No Solution
5. 
Solve for all possible values of [math]x[/math]: [math](sqrt(x+1))/(x+1)=sqrtx+1[/math]
  1. 0
  2. 0, 1
  3. All real numbers
  4. 1
6. 
Solve for all possible values of [math]x[/math]: [math](sqrt(x+3))/9=sqrt(x+1)[/math]
  1. [math]3, 9[/math]
  2. [math]-39/40[/math]
  3. [math]78/80[/math]
  4. [math]3[/math]
7. 
Solve for all possible values of [math]x[/math]: [math]sqrt(x+4)=4sqrt(4+x)[/math]
  1. All real numbers
  2. 4
  3. -4
  4. No Solution
8. 
Solve for all possible values of [math]x[/math]: [math](sqrt(x+6))/(sqrt(x-2))=(sqrt(4+x))/(sqrt(x-3))[/math]
  1. 4, 2
  2. [math]-4/3[/math]
  3. [math]3/4[/math]
  4. 10
9. 
Solve for all possible values of [math]x[/math]: [math]sqrt(x^2+4x-16)=4[/math]
  1. No Solution
  2. [math]-8, 4[/math]
  3. All real numbers
  4. [math]-4, 16[/math]
10. 
Solve for all possible values of [math]x[/math]: [math](3x+6)/(x+2) = x/3 [/math]
  1. No Solution
  2. -2, 9
  3. -2, 3
  4. 9

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